write 0 9 as a percentage

Percentage Calculator

Please provide any two values below and click the "Calculate" button to get the third value.

Percentage Calculator in Common Phrases

Percentage difference calculator, percentage change calculator, what is a percentage.

0.5 × 100 = 50

In other words, the ratio of 25 males to students in the classroom is equivalent to 50% of students in the classroom being male.

Percentage formula

Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values.

P × V 1 = V 2

If solving manually, the formula requires the percentage in decimal form, so the solution for P needs to be multiplied by 100 in order to convert it to a percent. This is essentially what the calculator above does, except that it accepts inputs in percent rather than decimal form.

Percentage difference formula

The percentage difference between two values is calculated by dividing the absolute value of the difference between two numbers by the average of those two numbers. Multiplying the result by 100 will yield the solution in percent, rather than decimal form. Refer to the equation below for clarification.

Percentage change formula

Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values then dividing the result by the initial value, essentially calculating how much the initial value has changed.

The percentage increase calculator above computes an increase or decrease of a specific percentage of the input number. It basically involves converting a percent into its decimal equivalent, and either subtracting (decrease) or adding (increase) the decimal equivalent from and to 1, respectively. Multiplying the original number by this value will result in either an increase or decrease of the number by the given percent. Refer to the example below for clarification.

EX: 500 increased by 10% (0.1) 500 × (1 + 0.1) = 550 500 decreased by 10% 500 × (1 – 0.1) = 450

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Decimal 0.9 as a percent

Decimal to convert

What is 0.9 as a percent?

The percent equivalent of 0.9 is 90%

How to turn a decimal 0.9 into a percent?

To express the decimal number 0.9 as a percent, follow these steps:

1. Multiply by 100: To convert a decimal to a percentage, you multiply the decimal by 100.

2. Add the Percentage Sign: After multiplying by 100, add the percentage symbol (%) to the result.

Thus, decimal 0.9 as a percentage is 90%

Related Calculations

• 90% as a decimal
• Number 90 Facts

Decimal to Percent Conversion Table

About "decimal to percent converter" calculator.

Introducing our user-friendly online decimal to percent calculator! With just a few clicks, you can effortlessly convert decimal values into their corresponding percentage equivalents.

For example, it can help you find out what is 0.9 as a percent? (The answer is: 90% ).

This handy tool simplifies the process of converting decimals to percentages, making it a breeze for anyone, whether you're a student working on math homework or a professional crunching numbers in your daily tasks.

Using our calculator is as easy as 1-2-3: Simply input the decimal value you want to convert into the designated field (for example, 0.9 ), then hit the 'Convert' button. In an instant, you'll receive the accurate percentage representation of your decimal input - 90%.

No more manual calculations or guesswork required. Our decimal to percent calculator ensures precision and saves you valuable time. Whether you need to find the percentage for a financial analysis, statistical report, or any other application, this tool has got you covered.

Experience the convenience and accuracy of our online decimal to percent calculator today, and make number conversions a breeze!

Percentage Calculator

How to use this percentage calculator, what is the percentage — how to find the percentage of something, how to find the percentage of two numbers — cookies 🍪, how to find the percentage of a number — other examples.

• How to calculate the percentage? What's the percentage formula?

History of percentage — the percent sign

Spelling — percent or per cent, what is per mille what is a basis point, percentage points (percent points), creating the percentage calculator.

This percentage calculator is a tool that lets you do a simple calculation: what percent of X is Y? The tool is pretty straightforward. All you need to do is fill in two fields, and the third one will be calculated for you automatically. This method will allow you to answer the question of how to find a percentage of two numbers.

Furthermore, our percentage calculator also allows you to perform calculations in the opposite way, i.e., how to find a percentage of a number. Try entering various values into the different fields and see how quick and easy-to-use this handy tool is. Is only knowing how to get a percentage of a number is not enough for you? If you are looking for more extensive calculations, hit the advanced mode button under the calculator.

Other than being helpful with learning percentages and fractions , this tool is useful in many different situations. You can find percentages in almost every aspect of your life! Anyone who has ever been to the shopping mall has surely seen dozens of signs with a large percentage symbol saying " discount! ". And this is only one of many other examples of percentages. They frequently appear, e.g., in finance, where we use them to find an amount of income tax or sales tax, or in health to express what is your body fat.

Keep reading if you would like to see how to find a percentage of something, what the percentage formula is, and the applications of percentages in other areas of life, like statistics or physics.

Our percentage calculator has four sections. The following instructions should help you select the right section and put it to good use:

The section What is p% of x? will calculate the given percentage of a number:

• Enter the percentage .
• Enter the number of which you need to find the percentage.
• The percent number appears at once.

For example, say you scored 80% on a test. If the test was for 30 marks, your score is 24 marks.

You can even calculate in reverse. This would allow you to, for instance, calculate your percentage based on your score. In a test for 30 marks, if you scored 27 marks, your percentage is 90%.

The section x is what percent of y? will determine the percentage of two given numbers:

Enter the number whose percentage you want to determine.

Provide the number against which this percentage must be evaluated.

The calculator gives you the percentage instantly.

For instance, say Gavin's rent is $1245 per month, while his monthly budget is $4000. When we enter 1245 in the first field and 4000 in the second, we can determine that his house rent takes up 31.125% of his monthly budget.

This section also works in reverse. Say Gavin wants to move to a place that costs no more than 25% of his monthly budget. When we input 25% as the percentage and 4000 in the second field, the calculator informs us that $1000 is the maximum rent Gavin can afford.

Enter the number for which you know the percentage.

Provide the percentage.

The calculator will give you the number you seek right away.

Let us see this with an example — 10 is 5% of which number? Enter 10 in the first field and 5% as the percentage. You can immediately see that the result is 200.

You can even use this in reverse. Entering 25% percentage and 50 in the third field, we learn that 12.5 is 25% of 50.

The section What is x increased/decreased by p%? will help you determine the effects of an increase or decrease in a value by a given percent:

Enter the initial value.

Select whether the change is an increase or decrease .

Enter the percent by which the initial value changes.

The changed value is displayed to you instantly.

For example, say that the price of a candy bar increased by 30%. Enter the original price, $5, in the first field. Next, choose that the change is an increase . Finally, enter 30% percent, and we learn the new price is $6.50.

It also works in reverse. Say we know the discounted price of an item is $44. If the discount is 10%, our calculator will tell us the original price is $48.89.

There is a lot of fascinating information about percentages in the following section, starting with what percentages are and how to find them. So grab some snacks and browse through it.

Percentage is one of many ways to express a dimensionless relation between two numbers (the other methods being ratios and fractions). Percentages are very popular since they can describe situations that involve large numbers (e.g., estimating chances for winning the lottery), averages (e.g., determining the final grade of your course), as well as very small ones (like the volumetric proportion of NO₂ in the air, also frequently expressed by PPM — parts per million).

One percent is a hundredth. As a percent sign, we usually use %, but sometimes it is denoted by pct . It means that 5 percent is the same as 5% , 5 pct , 0.05 , 5/100 , or five-hundredths . It is as simple as that, and this percentage calculator is a tool dedicated to working with decimal fractions and percentages. If you're seeking more complicated problems, try to figure out how to calculate the percentage of a percentage .

This is all nice, but we usually do not use percentages just by themselves. Mostly, we want to answer how big is one number in relation to another number? . To try to visualize it, imagine that we have something everyone likes, for example, a large packet of cookies (or donuts or chocolates, whatever you prefer 😉 — we will stick to cookies). Let's try to find an answer to the question of what is 40% of 20 ? It is 40 hundredths of 20, so if we divided 20 cookies into 100 even parts (good luck with that!), 40 of those parts would be 40% of 20 cookies. Let's do the math: 40/100 × 20 = 8 . A handy little tip: to divide by 100, simply move the dot two spaces to the left. In our calculation, 40/100 × 20 could be done as (40 × 20)/100 (it's the same thing). 40 × 20 is 800. By moving the dot in 800 by two digits to the left, you get 8.00, and when you get rid of all unnecessary zeros, you obtain 8 . In our calculator, enter 40 and 20 (so it reads "40% of 20" is 8).

A percentage is also a way to express the relation between two numbers as a fraction of 100 . In other words, the percentage tells us how one number relates to another. If we know that number A is 25% of number B , we know that A to B is like 25 is to 100, or, after one more transformation, like 1 to 4, i.e., A is four times smaller than B . This is what the percentage calculator teaches; what is a percentage and how to find a percentage of two numbers.

How to find a percentage of something? It's easiest to explain what is the percentage with cookies. It is surprising how often cookies save the day, right? Say we have a big drawer with 100 compartments (a 10 × 10 grid). Every compartment is one hundredth or 1% of the whole drawer. We then fill this drawer with cookies in a way that gives us exactly the same number of cookies in each compartment.

At first, let's start with the most straightforward example with 100 cookies . How to get the percentage of several, let's say, five cookies? It's easy: every compartment gets exactly one cookie. So one percent of 100 is one cookie , and five percent is five cookies.

Let's go with something a bit harder and four times more delicious: 400 cookies ! We're dividing them evenly, and every compartment gets four cookies. Cookies look smaller, but in our imagination, they are the same, just the drawer is much bigger! One percent of 400 is 4 . How about 15 percent? It's 15 compartments times four cookies — 60 cookies. Our tummies start to ache a little, but it has never stopped us from eating more cookies!

Now, something even harder — 250 cookies . Oh-oh, we divided up the first 200 cookies, placing two in every compartment. Now we are left with 50 cookies that need to be spread evenly, hmmm, it's half a cookie in every box. How to calculate the percentage? You are right — this time, 1 percent of the total number of 250 cookies is 2.5 . How many do we have in 15 boxes? 2.5 × 15 is 37.5.

So what is percentage good for? As we wrote earlier, a percentage is a way to express a ratio. Say you are taking a graded exam. If we told you that you got 123 points, it really would not tell you anything. 123 out of what? Now, if we told you that you got 82% , this figure is more understandable information. Even if we told you, you got 123 out of 150; it's harder to feel how well you did. A week earlier, there was another exam, and you scored 195 of 250, or 78%. While it's hard to compare 128 of 150 to 195 of 250, it's easy to tell that an 82% score is better than 78%. Isn't the percent sign helpful? After all, it's the percentage that counts !

What about decimal fractions and percentages? Percentages can easily be converted to decimals. Just divide the percentage by 100, and you are set. 15% is the same as 0.15. So as we have shown before, 0.15 of 250 cookies is thirty-seven and a half.

Percentages are sometimes better at expressing various quantities than decimal fractions in chemistry or physics. For example, it is much more convenient to say that the percentage concentration of a specific substance is 15.7% than that there are 18.66 grams of substance in 118.66 grams of solution. Another example is efficiency (or its special case — Carnot efficiency). Is it better to say that a car engine works with an efficiency of 20% or that it produces an energy output of 0.2 kWh from the input energy of 1 kWh? What do you think? We are sure that you're already well aware that knowing how to get a percentage of a number is a valuable ability.

While it's certainly quick and painless just to use our percentage calculator, you don't always have access to a computer or a smartphone. Also, it's just plain cool to be able to perform calculations in your head. Maybe not as cool as juggling flaming torches, but close.

The percentage tells you how number A relates to number B . A real-world example could be: there are two girls in a group of five children. What's the percentage of girls? In other words, we want to know what's the ratio of girls to all children. It's 2 out of 5, or 2/5. We call the first number (2) a numerator and the second number (5) a denominator because this is a fraction. To calculate the percentage, multiply this fraction by 100 and add a percent sign. 100 × numerator / denominator = percentage . In our example, it's 100 × 2/5 = 100 × 0.4 = 40 . Forty percent of the group are girls. That's the entire procedure of converting between decimal fractions and percentages.

Do you have problems with simplifying fractions? The best way to solve this is by finding the GCF (greatest common factor) of the numerator and denominator and dividing both of them by GCF.

Let's go the other way around and try to find the numerator . Say we know that 70 percent of fruits in the basket are apples, and there are 30 fruits altogether. It could be worse — they could be lemons. So how many apples do we have? Let's get our percentage formula: 100 × numerator / denominator = percentage . We want to find out the numerator. Let's move all the other parts of the equation to the other side. Divide both sides by 100 (to get rid of 100 on the left) and then multiply both sides by the denominator. This is what we get: numerator = percentage × denominator / 100 . Let's substitute percentage and denominator with our values: numerator = 70 × 30 / 100 . Now it's easy: numerator = 2100 / 100 = 21 , we have 21 apples. Should be enough for lunch or a rather violent food fight.

Now let's solve a problem with an unknown denominator . We spent 30 percent of our pocket money on bubble gum (we never said we're great investors). We bought 12 sticks for $1 each. So we know that $12 was 30 percent of our total budget. How much money did we have before we almost literally blew it all away? Let's start with our formula: 100 × numerator / denominator = percentage or 100 × 12 / denominator = 30 . This time we want to find out the denominator. Let's multiply both sides by the denominator and then divide by percentage. This way, we'll get 100 × 12 / 30 = denominator . And the other way around, denominator = 100 × 12 / 30 = 1200 / 30 = 40 . We had 40 dollars, and we spent 30 percent, or $12, on bubble gum. Totally worth it.

How to calculate the percentage? What's the percentage formula?

Staying with our cookie examples, let's name the three parts in our equation: the percentage of cookies — 40%, the whole pack of cookies — 20, and the part of the pack of cookies — 8. Depending on what you want to estimate, you can write three various percentage formulas:

• the equation for percentage is this: percentage = 100 × part / whole , and it answers the question "what percentage of 20 is 8".
• the formula for a part is: part = whole × percentage / 100 , and it answers "what is 40% of 20?".
• and finally, the formula for a whole is: whole = 100 × part / percentage , and it says "what is 100% if 8 is 40%?".

That's technically all. You should now know how to find the percentage of a number.

Although Ancient Romans used Roman numerals I , V , X , L , and so on, calculations were often performed in fractions that were divided by 100. It was equivalent to the computing of percentages that we know today. Computations with a denominator of 100 became more standard after the introduction of the decimal system. Many medieval arithmetic texts applied this method to describe finances, e.g., interest rates. However, the percent sign % we know today only became popular a little while ago, in the 20th century, after years of constant evolution.

The term percent is often attributed to Latin per centum , which means by a hundred . Actually, it is wrong. We got the term from Italian per cento — for a hundred . The percent sign % evolved by the gradual contraction of those words over centuries. Eventually, cento has taken the shape of two circles separated by a horizontal line, from which the modern % symbol is derived. The history of mathematical symbols is sometimes astonishing. We encourage you to take a look at the origin of the square root symbol!

Recently, the percent symbol is widely used in programming languages as an operator. Usually, it stands for the modulo operation. On the other hand, in experimental physics, the symbol % has a special meaning. It is used to express the relative error between the true value and the observed value found in a measurement. To know more about relative error, you can check our percent error calculator .

Have you ever met a percent symbol that had an additional circle? That's not a mistake! There are two related signs:

• ‰ — per mille — per thousand,
• ‱ — per myriad — per ten thousand (also known as a basis point),

Later in the text, we explain in more detail what per mille means, what is a basis point and how to convert per milles and basis points to percents.

Higher proportions use other notation (called parts-per notation), e.g., parts-per-million (PPM) which is frequently used to measure the concentration of a substance in solution or mixture. Of current concern is smog, the tiny particulate matter that enters the air and can seriously affect someone's health.

Percent or per cent? It depends on your diet. If you eat hamburgers for the majority of your meals, it is percent. If you prefer fish and chips, it is per cent. If you spray your fish-smelling chips with vinegar, then it is per cent, mate (as opposed to burger eaters' percent, dude). When it comes to percentage, both sides of the pond are in agreement: it should be a single word. Still confused? Americans say percent, British use per cent. Something tells us that American English is more popular nowadays, so this website uses a single-word form.

Per mille , per mil , per mill , or simply ‰ is similar to percent, only it is one thousandth ( 1/1000 or 0.001 ). If our household's budget is $2400 and we allocated 1 per mille of that to buying chewing gum, we would spend 2.4 dollars (2 dollars 40 cents) on annoying our teachers (well, 20 years ago it was not allowed in Polish schools. We do not know the rules nowadays 😃). It's pretty similar to how you find percentages. If you wanted to use percentage calculator to count per mille, simply use numbers 10× lower (0.2 instead of 2, 4 instead of 40).

Per myriad , basis point or just ‱ is one ten-thousandth( 1/10000 or 0.0001 ). It's 10× smaller than per mille, so to convert basis points to percents, you need to divide them by 100 . It's that simple!

Percentage points (or percent points ) are a rather tricky beast. We use it all the time even if we don't know it — and in these situations, we often incorrectly say percent instead of a percentage point . Once you read this section, you will know how to do it properly and be annoyed for the rest of your life (because other people will keep making the mistake).

Senator Homer Simpson was polling at 10% last month. He had a few successful debates since then, and now 12% of the population wants to vote for him. What's the change? You want to say 2%, are we right? It's wrong! Let's examine this. Imagine the whole population is 1000 people. 10% of them is 100. 12% is 120. What's the percentage increase? It's 100 × 20 / 100 = 20% !

This situation is when percentage points come in handy. We use percentage points when we want to talk about a change from one percentage to another. A change from 10% to 12% is two percentage points (or 20 percent).

Understanding changes in percentages can be done in two different ways:

• Change in percentage points (pp): The difference between two percentage values. If one value is 10 % and the other is 30 %, the change is 20 percentage points (20 pp).
• Change in percentage: The relative change between two percentage values. If one value is 10 % and the other is 30 %, the change is 200 % of the original 10 %.

Now, when you know everything about percentage points, we guarantee that you will read or hear other people incorrectly saying percent when they should be using percentage points. If you're anything like us, you will scream at the newspaper, insulting it in some made-up language. This reaction helps to free up space around you when you're using public transportation :-)

💡 The percentage difference calculator takes care of a very similar concept, used when we don't know the direction of the calculation (from number A to B or B to A).

Mateusz and Dominik are experienced in creating scientific tools that solve everyday problems and explaining the concepts in a simple, easy-to-digest manner. The idea for this percentage calculator was born when Mateusz was shopping online and comparing prices and discount percentages on different websites. Now, they use it not just to make better shopping decisions but to pick better investments.

We put extra care into the quality of the content to ensure they are as accurate and reliable as possible. Each tool is peer-reviewed by a trained expert and then proofread by a native speaker. If you’d like to learn more about our standards, please check the Editorial Policies page .

What is the percentage?

The percentage can be defined as the dimensionless ratio of two numbers. It can be used to compare two numbers and find out how much one is more than the other or compare the two numbers against a common scale.

How do I calculate x percent of y?

To calculate x percent of y:

• Divide x by 100.
• Multiply the previous result by y.

The resultant number is x% of y.

How much percent of y is x?

To find out x in terms of y:

• Divide x by y.
• Multiply the resultant number by 100.

The product of p% of y is equal to x.

How much is 60% of 1260?

60% of 1260 is equal to 756 . To calculate the 60% of 1260:

• Divide 60 by 100: 60/100 = 0.6
• Multiply the previous result by 1260: 0.6 × 1260 = 756 .

So, the 60% of 1260 is 756.

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Meat footprint, perfect square trinomial.

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Percentage Calculator

What do you want to calculate.

• Solve for Variable
• Practice Mode
• Step-By-Step

Example (Click to try)

How to calculate percentages.

• Convert percentage to a fraction with a denominator of 100.
• Multiply with the number that you want to get the percentage of.
• Reduce if necessary.

Decimal to Percent Calculator

Use this calculator to easily convert a decimal notation number to a percentage. Express a given decimal as a percent value.

Related calculators

• How to convert decimal numbers to percentages?
• Practical Examples
• Decimal to percent conversion table

    How to convert decimal numbers to percentages?

A percent was historically called "per cent", which is an abbreviated version of the Latin phrase "per centum" which literally means "per one hundred". Hence to calculate a percentage from a decimal number all that is needed is to multiply the number by one hundred and to append a percent sign (%). As this operation is simply to shift the decimal point (or comma) two positions to the right, it can be done simply for pretty much any number.

    Practical Examples

Take for example a loan interest rate of 0.05. To convert it to a percent, simply multiply by 100 and append (%): 0.05 x 100 = 5%. As described above, the operation can be performed by simply moving the decimal point two positions to the right. In this case this leaves no significant figures to the right of the decimal point so it can simply be skipped without loss of information.

In a different scenario, consider a growth rate of 1.5. It can be the growth of an asset or the spread rate of a virus. Regardless, to convert it to a percent value simply multiply by one hundred to get the result: 150%.

    Decimal to percent conversion table

The above table can be used by selecting the decimal from the left column and finding the corresponding percentage from the right column on the same row. For example, to see how much is 0.5 as percent, look up 0.5 in the "Decimal" column and examine the corresponding percentage value on the same row (50% in this particular case).

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Decimal to Percent Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/decimal-to-percent-calculator.php URL [Accessed Date: 15 May, 2024].

     Math calculators

Percentage Calculator

Calculate a percent of a value before and after, or find the percentage change between two values, and see how to calculate each one.

• Apply 10% to 100, and see how each value was calculated
• Try 12.5% of 50: the "50 less 12.5%" value is 43.75.
• Then try 12.5% of 43.75 (shows that before a 12.5% reduction it was 50.)
• Compare 100 to 110, and see that to go from 100 to 110 is a 10% increase, but to go from 110 back down to 100 is a 9.09% decrease (not a 10% decrease)

x% of y is the same as y% of x

Example: 10% of 15 is the same as 15% of 10

• 10% of 15 = 1.5
• 15% of 10 = 1.5

Percentage Calculator

LAST UPDATE: September 24th, 2020

Calculate Percent of a Number

Calculate what percent, calculate percent of what, more percentage calculators.

• Percentages
• Percentage increase
• Percentage decrease
• Percentage change
• Percentage error
• … see more percentage calculators

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• Solve equations and inequalities
• Simplify expressions
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Enter the value(s) for the required question and click the adjacent Go button.

PERCENTAGES

This section will explain how to apply algebra to percentage problems.

In algebra problems, percentages are usually written as decimals.

Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?

The number of questions correct is indicated by:

Ethan got 44 questions correct.

Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.

Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

Darrel’s grade for the course is an 89.6, or a B+.

b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?

The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.

So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.

Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.

a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).

Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

b. Simplify the equation.

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.

c. Solve the equation when the sale price is $97.

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)

The following diagram is meant as a visualization of problem 3.

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount

Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.

Study Tip: Remember to use descriptive letters to describe the variables.

CHAPTER 1 REVIEW

This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Informal Rules:

Adding or subtracting like signs: Add the two numbers and use the common sign.

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

Simplifying Algebraic Equations:

Combine like terms:

Solving Equations:

1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

c. If the call costs $23.50, how long were you on the phone?

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.

Percentages:

Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.

Math Topics

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• Add Fractions
• Simplify Fractions

• How to Calculate Percentages

Calculate Percentage

Enter two numbers and this calculator will compute what percent of the second number the first number represents to one thousandth of a percent.

Calculate Number Associated With a %

Enter a percent and a starting number and this calculator will figure the number associated with that percent of the initial number accurate to a thousandth.

Calculate Percent Change

Enter the starting number and the final number to computer what percent the first number changed to become the second number. This is useful for tracking price discounts, investment growth, or other things that change over time.

Here are instructions for the formulas to calculate common percent related math problems:

• formula: (x/y) * 100 = z%
• in words: divide x by y to get its decimal number & then multiply by 100 to convert the decimal into a percent
• formula z% / 100 * x = y
• in words: divide the desired resultant percent by 100 to convert it to a decimal, then multiply it by the original number to solve for the number which is associated with that percent of the original number
• formula: (y-x)*100/x = z% change
• in words: subtract the original number from the final number, multiply this result by 100 (move the decimal 2 places to the right) and then divide this value by the original number to get percent change

A Practical Guide to Pervasive Percentages

We might not notice it, but percentages are quite common in daily life. Even if your work does not involve a lot of computing or mathematical concepts, you’re bound to encounter it now and then. For instance, when you check your mobile phone, its battery life is expressed in percent. A retail store is offering up to 50% off on jeans till the end of the month. When you catch the news, the weather anchor says there’s 30% chance of rain in your area.

In its most literal form, percentages mean “part per hundred.” This is the expression of a fraction or ratio where the denominator is 100. The percentage became one of the most popular expressions of fractions for a reason. They illustrate proportion and completeness in a way that’s easy to understand. They also simplify the process of calculating based on a proportion. Percentages convert to decimals, which are much easier to process.

Its usefulness in everyday arithmetic is evident wherever you look. We see percentages everywhere. You can find them in banks and stores to video game inventories. They all mean something different in context, yet use the same expression. Grasping basic percentages is a vital skill that can help you save time and money. Besides convenience, this is especially true when it comes to expensive purchases and investments.

The Fundamentals of Percentages

Much like fractions, percentages represent parts of a whole. All percentages are numbers divided by 100. A single percentage point, 1%, is equal to the fraction 1/100. Thus, you can convert them into ratios, decimals, or other fractions. Likewise, you can express any fraction, decimal, or ratio as a percentage.

You have several ways of converting a fraction into a percentage. The easiest percentage conversion is through decimals. Divide the fraction to get its decimal value, then multiply it by 100.

(x/y) * 100 = z%

Where: x is the numerator y is the denominator  z is the percentage

For our first example, let’s find the percentage value of 6/8:

= (6 / 8) x 100% = (0.75) x 100% = 75%

When you already have the decimal value, move the decimal point two places to the left. Thus, 2% is 0.02 and 50% is 0.5.

Converting a percentage to a fraction or ratio is more complex. First, you must find the greatest common factor between the two numbers. Then you divide both the numerator and denominator by them. For instance, to simplify 5%, start by expressing it as 5/100. Then, divide the two numbers by their common factor, 5.

= (5 / 5) / (100 / 5) = 1/20

To convert to a ratio, change the slash into a colon.

Remember that your denominator is always 100, and not all numbers will share its factors. Often, you can simplify many percentages by leaving them as is. For instance, 37% will be 37/100 because the common factor between the two numbers is 1.

Here’s how we can turn 37.5% into a decimal, fraction, and ratio:

= 37.5% / 100 = 0.375

The fraction form of 0.375 is 375/1000. Let’s simplify this fraction. The common factor of the two numbers is 5. With this in mind, how simple can this fraction go?

= (375 / 5) / (1000 / 5) = 75/200 = (75 / 5) / (200 / 5) = 15/40 = (15 / 5) / (40 / 5) = 3/8  = 3:8

The Limits of Base 100

As a number, 100 is very convenient compared with varying fractions. You can divide evenly it by 1, 2, 4, 5, and 10, which are easy numbers to remember. But notice that it isn’t divisible by 3, 6, 7, and 9. Once you convert them, you encounter the awkwardness of repeating decimals . Rounded off to 4 decimal places, 100/3 is 33.3333(…).

To display these as exact values, you must express them as fractions. You can, of course, get an approximate answer by rounding it off. In most practical cases, it’s not an issue. Of course, you don’t need to fret at all if you deal with 99.9999(…)%. In the most familiar model of arithmetic , you can go ahead and say it’s 100% .

Both percentages and fractions are ways to describe ratio. Ratio can be defined as the numerical relation between two figures which shows the number of times one value is contained within the other. To help you visualize it better, imagine a whole box broken into 100 equal parts, where each part is equivalent to a single percent.

The following box represents the whole. It has 100 small boxes:

• Each small box is equal to 1% of the whole. The red box is 1%.
• Two boxes are equal to 2%. This represents the blue boxes.
• Five boxes are equal to 5%. This represents the green boxes.
• Twenty-five boxes are equal to 25%, which is 1/4 of the entire box. This represents the gray boxes.
• Fifty boxes are equal to 50%, which is 1/2 of the whole. This represents the yellow boxes.

Out of 100 colored boxes, 17 are white and 83 are colored. Thus, we can say that 17% of the box is white, while 83% of the box is colored.

Why do we use percentages? This concept makes calculating simpler when we’re working with parts of 100. Again, it’s easier than basing calculations on thirds, fifths, twelfths or other bases. It’s useful in particular because many fractions do not have a precise non-recurring decimal equivalent.

Thinking in terms of percentages also makes it easier to compare the amount of figures between each other. With a common denominator of 100, you’ll get a clearer idea of how much more or less a figure represents compared to another.

Applying Basic Percentage Calculations

For example, a classroom has 40 students. If we say 25% of the class are girls, you’ll get the idea that most of the students are boys (75%). That means out of 40 students, there are only 10 girls while there are 30 boys.

While it’s easy when you’re working with a figure that’s exactly 100, what about other numbers? In the example, the whole number is 40. We know that 50% or half of 40 is 20, and 25% or ¼ of 40 is 10. But how do we calculate this? Here’s the basic percent formula you can use:

Where: x = the part of the whole (numerator) y = the whole number (denominator) z = the percentage

*After dividing the part with the whole number, the figure is multiplied by 100 to convert the decimal number into its percentage form.

To easily compute percentage problems, use the above calculator on our page.

Let’s say a classroom has 40 students. 30 students are boys, while 10 students are girls. What % of the class are girls, and what % of the class are boys? Refer to the solution below.

Now, let’s say a class of 40 students had 25% girls and 75% boys. Then you’re asked to determine the precise number of boys and girls in the class. How do you do this? Simply change the formula a bit to solve for x:

(z% / 100) * y = x

At this point, you might be wondering if there is any relevance to knowing the ratio between boys and girls. Or if the ratio of anything is important at all. In reality, you encounter percentages a lot whenever you shop. Gone grocery shopping or bought anything lately? When you see discounts and markdowns, you immediately know you can purchase a product for a lower price. That % is based on the original price, which is the whole amount you would have paid if it weren’t for the discount. Nowhere is % more apparent when it comes to buying and finances. We’ll talk about this more in the latter sections of our article. 

A History of Percentages

The system of using percentages came long before the idea of decimals. People have used fractions to calculate taxation and tithes for millennia. It was the Ancient Romans , however, who popularized the use of fractions based on 100. The word itself comes from the phrase per centum . This means “by 100” in Latin, the Roman language.

During the reign of the Emperor Augustus (23 BCE – 14 CE), the Imperial government began to charge a tax on auctions. Called centesima rerum venalium , it cost 100th of the value of the goods sold. This tax helped pay for the retirement stipends of the Roman legionary army.

Long after Roman power faded in Europe, their influence remained strong. Educated people still used Roman numerals and divided things based on 100. By the Renaissance, wealthy merchants dealt with greater sums of money. Dividing by 100 simplified the need to keep track of their cash.

We can still see this today in the way we divide money. At present, most currencies are in decimals. Subdivisions of the U.S. dollar, for instance, are called cents , after the Latin word for 100. A single penny is one cent, or 1/100th of a dollar.

Did You Know?

When it comes to word usage, in American English, % is often written as one word, “percent.” However, in British English, % is commonly written as two words, which is “per cent.” But even in the British usage, the words percentage and percentile are written as one word.

The Percent Sign

It is forgivable to assume that the percentage sign "%" depicts a fraction. It does look like one at first glance, as does the division symbol, the obelus (÷). You may also question why the symbol has two zeroes in it. After all, isn’t dividing by zero undefined? Some sources claim that the two circles represent a shorthand for one hundred. That, while sort-of true, is not the whole story. The story behind it is much more complex.

Much like the ampersand (&), the percentage sign began as a shorthand of a phrase. The symbol was unknown before 1425. Back then, people in Europe expressed percentages in an abbreviation called pc o . This is the shorthand for the phrase per cento , the Italian version of the original Latin phrase.

Other writers sometimes added a line under the p (ꝑ) to show its use as an abbreviation. By the 1600s, the shorthand evolved into a glyph; the c turned into a circle, which rested on top of a line. The o became the bottom circle. Over time, writers began using just the glyph, which resembled an obelus. Incidentally, it was around the same time when the obelus was used as a symbol for division. 

The two circles, together with the line, represent the number 100. By the 1800s, the modern percent symbol dropped the p abbreviation that preceded it. Writers also slanted the line between the two circles.

The Permille and Permyriad

Its resemblance to a fraction didn’t go unnoticed, though. Soon, the percentage sign led to a set of symbols representing multiples of 10. One symbol, the permille sign (‰), emerged to depict parts per thousand. Meanwhile, the permyriad (‱) measures parts per ten thousand.

Both are found in specific circumstances. Scientists use permilles in measuring trace amounts in solutions. The concentrations in these cases are very low. Permyriads, meanwhile, find use in the realm of finance. Financial professionals use them to measure basis points, which are far lower than percentage points.

Percentages as a Measurement

Comparing portion sizes is one key to the popularity of percentages. People find it easier to compare percentages than fractions. This is the reason why third pound burgers never quite took off in the United States. The target audience didn’t realize that these were heavier than quarter pound burgers. Thus, even marketing departments often use percentages over fractions to tout larger sizes.

People use percentages to compare things in three different ways:

• Measuring changes in size: Percentages measure how much a thing changed in size or value relative to how it was before. For instance, an investor’s portfolio may have grown in size by 4% of its original value over the past year.
• Measuring differences in rates: You can measure the difference between rates from two periods via percentage points. Experts use the changes in growth rates to measure national economic performance. If the growth recorded is positive, it indicates rising growth.
• Measuring differences in proportion: Percentages distinguish between population subsets and measure their size relative to the whole. Market researchers, for instance, use these to determine brand popularity. They can, for example, say that a brand of soap is the most popular if at least 51% of the population prefer it.

Each of these comparisons derive the percentage in different ways. When measuring changes in size, you compare the difference between the new value and the old one. In our first example, let’s assume that the investor’s starting principal is $2,000. If the growth is 4%, here’s how much they made over the year.

= $2,000 x 4% = $2,000 x 0.04 = $80

Finding the difference in rates is more complex. In our second example, let’s assume that the country’s gross national product grew by 2%. This year, it grew by 2.5%, a change of 0.5 percentage points. This number seems unimpressive at first glance, but is it? Thus, we must look below the surface. How much did the percentages change? Let’s find the percentage change through the following formula:

[(y – x) * 100] / x = z%

Where: y is the present value x is the previous value z is the percent change of these values

= [(2.5 – 2) * 100%] / 2 = [0.5 * 100%] / 2 = 50% / 2 = 25%

Analyzing changes in percentages puts things in perspective. While this year’s GDP grew 0.5% higher than last year, it represents a 25% change in growth rates over that period. And because economies are large, even these tiny changes can spell good (or bad) news for everyone. 

Before you begin, find out the total number of people in the population set or sample. Next, you record the number of each of the responses within the set. In our third example, the product survey, we’ll assume the following details:

• A population size of 5,000 respondents
• Three different soap brands (brands X, Y, and Z)

Here’s the tally of the number of responses for that survey:

Taken together, those who prefer other brands or no brands in particular comprise 39.48% of the sample. In most cases, the total percentage will tally to exactly 100%. In some statistical situations, the percentages may fall short or exceed 100% . When the tally falls short, this is often because of rounding. Overshooting, meanwhile, is often the result of people identifying with more than one option.

A rate is a ratio that compares two distinct units. In its most common form, it is a charge based on another amount. Fuel efficiency rates, for instance, measure the distance your vehicle can travel for every unit of fuel it consumes. If a car reaches 50 miles per gallon, it is far more efficient than a car that goes 25 miles per gallon. This becomes essential when calculating how much you spend on fuel with each trip.

In finance, economics, and statistics, rates are expressed as percentages. These state the amount of growth over a specific period. Interest rates, for instance, refer to the fee you must pay each year for the amount of money you borrowed.

Bigger than a Hundred

In everyday speech, people mention percentages greater than 100 as a convenient hyperbole. When you give 150%, it indicates a level of dedication far beyond what’s needed. People do use percentages above 100 in a literal context.

Often, they involve measuring exponential growth or size differences . A 50% growth rate, for instance, indicates that something grows by half its size or value. A rate of 200% shows growth that’s twice the original value, and so on.

When you do find percentages expressed in the hundreds, it will sound alarmist. It likely is for a good reason. Anything that grows twice its size in a short span is worth paying attention to. If, for instance, your sales grew by 400% last year, you must re-examine how you did it. Meanwhile, if your debts grew by 400%, you must re-evaluate your financial strategy .

Common Percentage Mistakes

We tend to misunderstand percentages , especially for something we use all the time. Fortunately, we can avoid some of the most egregious missteps. A good way to avoid mistakes is to clarify how we use percentages in a given context.

One common error is when interpreting percentages is when measuring growth. For instance, let’s assume you and your company sold 10,000 bags of cake flour in 2019. In 2020, that number increased by 60,000 bags. It’s tempting to say that your sales grew by 600%.

Sure enough, your total sales in 2020 are 600% of your sales the year before. But that’s not how much your sales grew. To measure growth, start instead with a base amount and subtract it from the present amount. Our base amount is the volume of sales in 2019. Here’s how much your sales have changed.

= (60,000 – 10,000) / 10,000 = 50,000 / 10,000 = 500%

While you sold 600% more units, your annual growth was 500%. This represents the sales above those needed to match the previous year’s numbers. Bear your starting and ending points in mind when calculating percentage growth.

Another common mistake is interpreting differences in percentages. Sometimes, readers jump to conclusions without looking at the percentages up close. We’re tempted to think that a greater value indicates a greater percentage growth. But that’s not always the case. For instance, suppose that the price of a video game went up from $15 to $30 one year. The following year, it increased to $50.

On the surface, it’s easy to think that the second year had a higher percentage of growth. After all, the price increase of the second year (20) is bigger than the first’s (15). But think again. In the first year, the price grew by 100%.

= (15/15) x 100% = 1 x 100% = 100%

The following year, the price grew only by 66.67% or a third.

= 20/30 x 100% = 0.6667 x 100% = 66.67%

You may also encounter ambiguity expressing percentage changes in a sentence. We can see this in action when discussing interest rates. Let’s assume the present interest rate was 2%. If the rate increased by 5%, what does this mean? Most laypeople will assume that it means it increased to 7%. However, it can also mean that it increased by 5% of 2%. This leads to the total of 2.01%, which is a lot less impressive.

Whenever possible, use clear terms to avoid ambiguity. In our example, it’s better to say that the rate changed by 5 percentage points, rather than by 5%. 

Remember: Percentages never cancel out .

Here’s another common example. Let’s say you increased a number by 30%, then reduced it by another 30%. You might expect to end up with the same number you started with. But you don’t . This assumption is incorrect.

Given how we base percentages on a 100 denominator, it’s understandable why this is confusing. We tend to presume we are starting with the same whole number. When in reality, increasing or decreasing that number has changed the basis for the percentage.

For a simpler example, say you have 100 objects and decreased that by 30%. You are left with 70 objects.

= 100 – 30% = 70

Now, if you increase 70 by 30%, you get 91. Notice that it does not restore the number of your objects to 100. This is because 30% of 70 is equal to 21.

= 70 + 30% = 91

In the first part, we took 30% of 100. In the second part, we took 30% of 70. Again, the basis for the percentage changes each time you increase or decrease its value. Take note of this to avoid making the same mistake.

Working with Populations

Percentages are an important component of analyzing statistical data. These let you show the differences in the subsets of a population with relative ease. They also serve as a template for visual aids. You can use the fraction method above to find the percentage of a subset relative to the population size.

Working backwards, you can find the value a percentage as long as you know the size of the population. To find the numerical value of the percentage, use this formula:

z% / 100 * x = y

Where: x is the population or sample y is the subset z is the percentage

Let’s see this in action. Suppose you’ve read an article on the local news that says 12% of respondents prefer pineapple on a pizza. Most news articles will not provide the tabular data of surveys like this. They might, however, mention the population size of that survey. In our example, the article mentions that the surveyors interviewed 5,000 people. Without looking at the study’s data, we can determine how many people gave that answer:

= (12% / 100% ) x  5,000 = 0.12 x 5,000 = 600

To make an accurate assessment, we must know the size of the sample the percentage comes from. Can the sample represent the population at large? Only if it’s big enough. For instance, brands love touting that “9 out of 10 people” recommend them. If they only had a sample size of 10 people, that’s not definitive.

Quantity Comparison

Proportions matter when you’re making chemical formulations. To achieve the desired results, you must use the appropriate proportions of ingredients. To create a bigger batch, you must double the ingredients according to their proportion. Knowing these percentages will help you create a consistent product.

This becomes especially important when dealing with active ingredients. During COVID-19 pandemic, for instance, hand sanitizer has become hard to find. So, a lot of people began searching for ways to make it themselves. According to the Centers for Diseases Control and Prevention (CDC), hand sanitizer must comprise at least 60% alcohol to be effective . If you start off with a 99 percent alcohol solution, you can use 2/3rds of it in a mixture. The resulting hand sanitizer will be 66 percent alcohol, well within CDC parameters. If you start with a 70% commercial alcohol solution, however, the resulting mixture will be much too low.

You also need exact measurements when you’re baking. To get the desired texture and consistency, you must make sure you only use the amounts you need. It can be hard to determine precise measurements for non-fluid ingredients. Thus, bakers have a specific system to measure percentages based on the weight of the ingredients.

Sales Tax, Discounts, & Coupons

Percentages first came into widespread use to make calculating taxes easier. Even today, the government measures taxes in percentages. In many places, there’s a value-added tax on retail items. In some places, retailers do not add sales taxes into the final price. Thus, it can be a rude surprise when you get to a checkout. This can make it rather difficult to stay on a budget.

Using percentages, you can derive the extra you might add to the price. Learn the rates of your local and state taxes and apply them each time you buy.

Retailers jostle for your attention by marking down their prices using percentage discounts. On the surface, they can be very tempting. How good a deal they are depends on the size of the discount. A price cut that’s 20% off is good, depending on the item you’re buying. A 50% discount, when you can find one, is even better.

Even when you’re not on a budget, don’t forget to calculate discounts and coupons when you’re shopping. Whether you’re buying an expensive gadget, a simple item, or groceries, it’s still better to save several bucks (or even a hundred) than none at all.

Let’s suppose you’re looking for a new pair of running shoes. Luckily, the apparel store put 30% off on their shoes. And you, being a wise shopper, also saved a coupon for 15% off on any item. The store allows you to use the coupon even if the shoes already have a discount. If the running shoes you want costs $80, how much would it cost with the discount and coupon?

If you’re not used to calculating in percentages, you might think 30% and 15% off would mean 45% off. This is wrong . Percentages do not work that way . What you do is take 30% off and compute it with the original price. Then, you take 15% off from the coupon and also compute it with the original price.

First, ask what is 30% of $80? Convert the percentage to decimal and solve it like this:

= 0.30 x $80 = $24

Now you know $24 is the discount amount. We then subtract this amount from the original price.

= $80 – $24 = $56

With 30% off, the sale price for the running shoes is $56. Now, let’s solve the 15% off coupon discount.

= 0.15 x $80 = $12 = $56 – $12 = $44

Since the running shoes’ sale price is $56, we’ll subtract $12 from this amount. From an original price of $80, because of the discount and coupon, the running shoes are now only $44 . But hold on right there. Most states in the U.S. impose sales tax, and this applies to retail purchases. As of this writing, only five states currently do not enforce sales tax: Oregon, Montana, Delaware, New Hampshire, and Alaska.

Using our previous example, let’s suppose the sales tax on retail is 9%. To calculate this, the tax is based on the item’s sale price . So we should ask, how much is 9% of $44?

= 0.09 x $44 = $3.96

$3.96 is the sales tax. Now, we add this tax to the sales price.

= $44 + $3.96 = $47.96

From an original price of $80, the running shoes now cost $47.96. After discounts and the sales tax, you actually save $32.04 on your purchase.

Giving Tips at Restaurants

It’s important to know how much tip you’ll give in a restaurant. This way, you’re not giving too much or too little to your waiter. Depending on where you’re dining, make sure to research the average tipping rate. According to Consumer Reports , for starters, a basic rule in restaurant tipping is to leave between 15% to 20% of your total pre-tax restaurant bill. Never leave below 15% unless you believe the service was really bad. If your server was rude or offensive, speak to the manager. This feedback will help improve the establishment’s customer service.

For example, you dined out with two friends and split the bill equally. Your total bill was $89.50 and you intend to give a 20% tip. You can calculate the tip before or after you split the bill. Since it’s a real-life scenario, it’s acceptable to round the total bill to $90. Its easier to split it in thirds this way.

Federal Income Tax Rates

Percentages matter when tax season rolls in. This is where things can get complex. For instance, the U.S. Federal government charges a progressive tax rate on incomes. The government divides income tax rates based on brackets. People with higher incomes owe higher taxes.

Those who fall on a higher tax bracket don’t need to pay the higher rate on all their income, though. They first must pay the lower rate for the part of their income that falls under the first bracket. Then, they pay the higher rate on the remaining income.

For example, in 2021, U.S. Federal marginal tax rates are as follows:

For instance, you and your spouse file jointly and make $25,000 a year. You will pay only 10% in taxes on the first $19,990 of your income and 12% for the remaining $5,100.

In this system, even the biggest earners pay the lowest rate on a part of their income. This makes taxation complex, but it has its perks. You don’t need to worry about paying a higher percentage when you get a raise.

While federal tax is based on income, the government allows you to make tax deductions on your taxable income. This means you are not required to pay tax on your total annual earnings. By law, you are entitled to a standard deduction based on your filing status. Just take note that not all personal expenses are eligible for deductions. The IRS specifies which costs you can deduct from your income.

The standard deduction is adjusted every year to keep up with inflation. For example, in 2021, filers who are single have a standard deduction of $12,550, while those who are married filing jointly (below 65 years old) have a standard deduction of $25,100. But for tax year 2020, single filers had a standard deduction of $12,400, while those married filing jointly had a standard deduction of $24,800.

Remember, maximizing deductions help lower your tax bill . If you take advantage of enough deductions, you can even reduce your tax rate for the year. For example, in 2021, let’s say you’re single and earned $47,000 for the year. When you estimated your deductions, it amounted to $7,000, which lowers your taxable income to $40,000. Based on the table above, from a tax rate of 22% at $47,000, your tax rate is reduced to 12% at $40,000.

What does this mean? If your taxable income stayed at $47,000, your tax bill would be a steep $10,340. However, because you maximized your deductions, your taxable income is reduced to $40,000. This lowered your tax bill to $4,800. Thus, you’ll save a total of $5,540 on taxes.

Interest Rates in Loans and Credit Cards

To build our lives, we make use of consumer credit for major purchases. Since a house and a car are very expensive propositions, you likely need a mortgage and auto loan to afford them. Most people also use credit cards to afford important expenses now and then pay for them later on.

When it comes to consumer credit, be mindful of the interest rate . This is the fee lending institutions charge to keep your loans serviceable. For mortgages, car loans, and credits cards, the interest is based on the annual percentage rate (APR), which is a portion or your loan amount. The interest rate determines the interest charges you must pay over the duration of your loan. Moreover, borrowing a larger loan amount will result in more expensive interest costs.

Mortgage Rates

Here’s an example comparing mortgage rates. Suppose you want to buy a $300,000 house and saved $60,000 for down payment. This leaves your total loan amount (principal) to $240,000. You’re looking to get a 30-year fixed-rate mortgage. While searching, you’re offered 4.5% and 3.8% APR. How much monthly payment and total interest will you pay for each option?

For this example, we’ll use our mortgage calculator to find the total interest costs.   

30-year Fixed-rate Mortgage Home price: $300,000 Down payment: $60,000 Loan amount: $240,000

*This calculation did not include escrow costs.

Based on the results, it’s a no-brainer you should get a lower interest rate. But how much can you save? If you get the 4.5% offer, your monthly payment will be $1,216.04 and your total interest charges would be $197,776.11 over the life of the loan. But with the 3.8% offer, your monthly payment will be $1,118.30, which is $97.74 cheaper than the previous offer.

Savings are more evident when we compare interest costs. With 3.8% APR, your total interest charges amount to $162,587.15. This saves you $35,188.96 on interest costs. Thus, you literally save thousands of dollars over the life of the loan just by securing a lower rate.

Credit Card Interest Rates

Next, let’s talk about credit cards. If you have a credit card balance from month to month, you should pay it ASAP . Unlike mortgages and car loans with fixed terms, credit card debt is harder to pay down. Left unpaid too long, this can spiral into toxic debt because of compound interest .

When it comes to paying debt, compound interest is not your friend. If you don’t pay your balance for the month, you end up paying interest on interest that it accrues. This interest is calculated continuously and added to your balance, which you also pay interest on. In other words, it keeps compounding. For instance, if you owe $1,000 and your interest is compounded each month at 10%, after the first month, you’ll owe $1,100. Right after the second month, you’ll owe $,1210, and so on. If you have late payments, you might also deal with expensive late fees . So be sure to pay off your balance as soon as you can.

Furthermore, credit cards are a form of unsecured debt, which means it does not use any collateral such as a house to guarantee the loan. Thus, credit cards typically impose higher interest rates than secured debt. As of May 5, 2021, CreditCards.com state that the average APR of a brand-new credit card is 16.15%. And depending on your credit score, rates can range from 13% to as high as 35%. Thus, avoid using credit cards for large expenses, unless you really need to for emergencies. Even then, make sure to pay it as soon as you can.

Important Tip!

To steer clear of compounding debt, be sure to pay your credit card balance in full every month. Diligently do this on or before the due date. The idea is to only purchase what you can afford, and to make sure you pay it in full each month. By settling your total credit card balance before interest is charged, you can avoid compounding debt. This method is called playing the float . You can only apply this strategy if you do not have any outstanding credit card balance.

Money Matters

Percentages play a crucial role in finance. Big picture percentages play a pivotal part in the fate of your personal finances. Inflation rates, for instance, show how fast your money loses value.

The financial system is built upon interest. Percentages measure the rates these fees are paid. Lenders and financial institutions base interest on specific rates. Investors receive interest on their savings accounts and investments. In exchange, companies and banks use these funds for revenue-generating enterprises. Banks, in turn, make money from the interest they earn from loans and credit.

On a smaller level, understanding percentages is essential to securing your financial future. In general, you’d want a higher rate for your savings and investments. In turn, you must find the lowest rates you can when you borrow money. Looking at percentages is but one of many factors to consider in personal finance. To know more, check out our guides on our debt management and compound savings calculators.

• Trigonometry
• Percent Off
• Statistical Average
• Standard Deviation
• Correlation
• Probability
• Log/Antilog
• Critical Value
• HEX & Binary
• Weight/Mass
• Temperature
• Current Time
• Time Duration
• Balance Equations

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