# Percents: Converting Percentages, Decimals, and Fractions

#### Lesson 4: Converting Percentages, Decimals, and Fractions

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### Converting fractions, decimals, and percents

When we talk, we frequently use different words to express the same thing. For exemplar, we could describe the lapp car as tiny or little or small. All of these words mean the car is not boastfully. Fractions, decimals, and percents are like the words tiny, little, and small. They ‘re all just unlike ways of expressing parts of a whole .
In this image, each measuring cup has the like total of juice in it. But we ‘ve expressed this measure in three ways : as a fraction, as a percentage, and as a decimal. Since they ‘re expressing the lapp amount, we know that 1/2, 50 %, and 0.5 are equal to each other. any prison term we see 1/2, we ‘ll know it can besides mean 50 % or 0.5.

sometimes it ‘s useful to convert one kind of number into another. For model, it ‘s much easier to add 1/4 and 0.5 if you turn 0.5 into a fraction. Learning how to convert fractions, decimals, and percents will besides help you as you learn more advanced mathematics .

### Fractions and decimals

Every fraction can besides be written as a decimal, and vice versa. You may not do this very much, but converting decimals and fractions can help you in mathematics. For example, it ‘s easier to subtract 1/6 from 0.52 if you turn 1/6 into a decimal first .

#### Converting a fraction into a decimal

Let ‘s convert a divide into a decimal. We ‘ll be using a mathematics skill you ‘ve already learned : long division. To refresh your memory on this skill, you can review our Long Division lesson .
Click through the slideshow to learn how to convert a fraction into a decimal .

• Let ‘s see how we can convert 1/4 into a decimal fraction .
• To convert a fraction into a decimal fraction, we ‘ll just divide the numerator …
• To convert a fraction to a decimal fraction, we ‘ll good divide the numerator … by the denominator .
• In our exercise, we ‘ll divide 1 by 4 .
• 1 divided by 4 equals 0 .
• To keep separate, we ‘ll add a decimal point and a zero after the 1 .
• We ‘ll besides add a decimal point after the 0 on top .
• now we can divide 10 by 4 .
• 10 divided by 4 equals 2 .
• now we ‘ll multiply 4 by 2 .
• 4 times 2 equals 8. So we ‘ll subtract 8 from 10 .
• 10 minus 8 equals 2 .
• Since 2 is greater than 0, we ‘re not finished separate even. We ‘ll add another 0 after the decimal degree and bring it down .
• now we ‘ll divide 20 by 4 .
• 20 divided by 4 equals 5 .
• now we ‘ll multiply. 4 times 5 equals 20 .
• When we subtract 20 from 20, we get 0. The 0 means we ‘re done divide .
• 1 divided by 4 equals 0.25 .
• sol 1/4 is peer to 0.25 .

#### Try This!

Convert each of these fractions into a decimal .

#### Converting a decimal into a fraction

immediately we ‘ll do it in reverse. Let ‘s convert a decimal into a fraction .
Click through the slideshow to see how to convert a decimal into a fraction .

• We ‘re going to rewrite 0.85 as a divide. To convert a decimal into a fraction, we ‘ll use place values .
• In decimals, the total immediately to the right of the decimal item is in the tenths place .
• The place to the right of the one-tenth place is the hundredths place .
• To convert a decimal, first base we ‘ll check the place respect of the last number to the correct .
• In 0.85, 5 is in the hundredth target .
• This means our decimal fraction is equal to 85 hundredths. 85 hundredths can besides be written as 85/100 .
• now we have our divide. But it ‘s always a good idea to reduce fractions when we can—it makes them easier to read .
• To reduce, we need to find the largest number that will go evenly into both 85 and 100 .
• 5 is the largest count that goes evenly into 85 and 100. So we ‘ll divide both parts of our fraction by 5 .
• first we ‘ll divide the numerator. 85 divided by 5 equals 17 .
• nowadays we ‘ll divide the denominator. 100 divided by 5 equals 20. This means 85/100 can be reduced to 17/20 .
• therefore 0.85 is equal to 17/20 .

Reducing a fraction may seem unnecessary when you ‘re converting a decimal fraction. But it ‘s crucial if you ‘re going to use the fraction in a mathematics trouble. If you ‘re adding two fractions, you may even need to reduce or change both fractions so they have a common denominator .

#### Try This!

Convert these decimals into fractions. Be surely to reduce each fraction to its simplest form !

### Percents and decimals

Knowing how to convert percents and decimals will help you calculate things like sales tax and discounts. To learn how, check out our Percentages in real Life example .

#### Converting a percent into a decimal

Converting a percentage into a decimal fraction is surprisingly comfortable. It only takes a few simple steps .
Click through the slideshow to learn how to convert a percentage into a decimal fraction .

• We ‘re going to convert 17 % into a decimal fraction .
• first base, we ‘ll take the percentage signboard …
• first, we ‘ll take the percentage polarity … and turn it into a decimal point .
• following, we ‘ll move the decimal point two spaces to the left .
• now we ‘ll move the decimal point two spaces to the left .
• We ‘ve converted our percentage to a decimal fraction. 17 % is equal to 0.17 .
• Let ‘s search at another case. This time we ‘ll turn 78 % into a decimal fraction .
• first, we ‘ll replace the percent sign with a decimal point .
• then we ‘ll move the decimal fraction point two spaces to the left .
• then we ‘ll move the decimal fraction point two spaces to the left .
• 78 % is peer to 0.78.
• Let ‘s attend at another exemplar. This time we ‘ll turn 8 % into a decimal .
• first, we ‘ll replace the percent sign with a decimal point .
• then, we ‘ll move the decimal point two spaces to the left .
• then, we ‘ll move the decimal bespeak two spaces to the left .
• Notice there is an extra space next to the 8. We ca n’t good leave an exposed space with nothing in it. Since zero equals nothing, we ‘ll replace the space with zero .
• Notice there is an extra space next to the 8. We ca n’t just leave an overt space with nothing in it. Since zero equals nothing, we ‘ll replace the space with zero .
• 8 % is equal to .08

#### Why does this work?

Converting percents into decimals is so easy that you may feel like you ‘ve missed something. But do n’t worry—it very is that bare ! here ‘s why the method acting we showed you works .
When we turn a percentage into a decimal, we ‘re actually doing two steps. First, we convert our percentage into a fraction. Since all percents are out of 100, we just put the percentage over 100, like this :
78 % = 78/100
In the moment footstep, we convert 78/100 into a decimal. You already know this means we ‘ll divide the numerator by the denominator, like this :
78 ÷ 100 = 0.78
indeed why did n’t we show you these steps in the slideshow ? Because you can get the answer without them. You know that all percents are out of 100, so you can skip making the percentage into a fraction. You have to divide the percentage by 100 to get a decimal, but there ‘s a flying way to do that. equitable move the decimal point two spaces to the left ! This direction, you can get the lapp solution with just one easy step .

#### Try This!

Convert these percents into decimals .

#### Converting a decimal into a percent

now we ‘ll reverse what you precisely learned. Let ‘s convert a decimal into a percentage .
Click through the slideshow to see how to convert a decimal into a percentage .

• We ‘re going to convert 0.45 into a percentage .
• We ‘ll reverse what we did in the last segment. This time, we ‘ll move the decimal fraction point two places to the right .
• We ‘ll reverse what we did in the last department. This time, we ‘ll move the decimal point two places to the right .
• now we ‘ll replace the decimal target with a percentage sign .
• We ‘ve finished converting our decimal fraction into a percentage. 0.45 is peer to 45 % .
• Let ‘s try another model. This clock our decimal has three numbers to the right of the decimal point .
• But we ‘re even going to move the decimal sharpen two spaces to the right .
• But we ‘re still going to move the decimal detail two spaces to the right .
• We inactive have a number to the right of the decimal fraction orient. The number isn’t a 0, so we ca n’t drop it .
• alternatively, we ‘ll keep the decimal charge and add a percentage sign at the goal of the number .
• thus 0.635 is equal to 63.5 % .

#### Try This!

Calculate these decimals as percents .

### Percents and fractions

Knowing how to write percents as fractions and frailty versa can help you in your casual life. For example, let ‘s say you earned a grad of 80 % on a test. You can convert 80 % into a fraction to find out how many of your answers were correct. When your teacher grades the test, she may do the opposite. If a scholar got 8 out of 10 questions right, the teacher can convert 8/10 to a percentage to give the scholar a grad .

#### Converting a percent into a fraction

When you ‘re converting a percentage into a fraction, it helps to remember that percents are constantly out of 100. You can practice with percents in our introduction to Percentages moral .
Click through the slideshow to learn how to convert a percentage into a divide .

• We ‘re going to convert 30 % into a fraction .
• In Introduction to Percents, you learned that all percents are out of 100. In fact, that ‘s what the password percent means .
• sol any percentage is equal to itself over 100. In our model, 30 % is adequate to 30/100 .
• now we ‘ve converted 30 % into a divide, but we still need to reduce it .
• 10 is the largest number that goes evenly into 30 and 100. So we can divide both parts of the divide by 10 .
• We ‘ll divide the numerator of the divide foremost. 30 divided by 10 equals 3 .
• nowadays we ‘ll divide the denominator. 100 divided by 10 equals 10 .
• then 30 % is peer to 3/10 .

#### Try This!

Write these percentages as fractions. Make sure to reduce each divide to its simplest mannequin .

#### Converting a fraction into a percent

Converting a fraction uses two of the skills you barely learned : writing a fraction as a decimal, and writing a decimal as a percent. Let ‘s see how we can use these skills to convert a divide into a percentage .
Click through the slideshow to learn how to convert a fraction into a percentage .

• Let ‘s convert 3/6 into a percentage .
• fair like when we converted a fraction into a decimal fraction, we ‘ll divide the numerator by the denominator .
• 3 divided by 6 equals 0.5 .
• We ‘ve turned our fraction into a decimal fraction .
• now we ‘ll turn the decimal into a percentage by moving the decimal point two spaces to the right .
• now we ‘ll turn the decimal into a percentage by moving the decimal decimal point two spaces to the right .
• We ‘ll besides change the decimal point into a percentage sign. 0.50 is equal to 50 % .
• sol 3/6 is peer to 50 % .

#### Try This!

Convert these fractions into percents .

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