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#### Lesson 5: Converting Percentages, Decimals, and Fractions

### Converting fractions, decimals, and percents

### Fractions and decimals

#### Converting a fraction into a decimal

#### Try This!

#### Converting a decimal into a fraction

#### Try This!

### Percents and decimals

#### Converting a percent into a decimal

#### Why does this work?

#### Try This!

#### Converting a decimal into a percent

#### Try This!

### Percents and fractions

#### Converting a percent into a fraction

#### Try This!

#### Converting a fraction into a percent

#### Try This!

### Assessment

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When we talk, we often use different words to express the same thing. For example, we could describe the same car as **tiny** or **little** or **small**. All of these words mean the car is not big. Fractions, decimals, and percents are like the words **tiny**, **little**, and **small**. They're all just different ways of expressing **parts** of a **whole**.

In this image, each measuring cup has the same amount of juice in it. But we've expressed this amount in three ways: as a fraction, as a percent, and as a decimal. Since they're expressing the same amount, we know that 1/2, 50%, and 0.5 are equal to each other. Any time we see 1/2, we'll know it can also mean 50% or 0.5.

Sometimes it's useful to convert one kind of number into another. For example, 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 also help you as you learn more advanced math.

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

Let's convert a fraction into a decimal. We'll be using a math 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.

Convert each of these fractions into a **decimal**.

Now 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.

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

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

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 lesson.

Converting a percent into a decimal is surprisingly easy. It only takes a few simple steps.

Click through the slideshow to learn how to convert a percent into a decimal.

Converting percents into decimals is so easy that you may feel like you've missed something. But don't worry—it really is that simple! Here's why the method we showed you works.

When we turn a percent into a decimal, we're actually doing two steps. First, we convert our percent into a fraction. Since all percents are out of 100, we just put the percent over 100, like this:

78% = 78/100

In the second step, 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

So why didn'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 percent into a fraction. You have to divide the percent by 100 to get a decimal, but there's a quick way to do that. Just move the decimal point two spaces to the left! This way, you can get the same answer with just one easy step.

Convert these percents into decimals.

Now we'll reverse what you just learned. Let's convert a decimal into a percent.

Click through the slideshow to see how to convert a decimal into a percent.

Calculate these decimals as percents.

Knowing how to write percents as fractions and vice versa can help you in your everyday life. For example, let's say you earned a grade 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 student got 8 out of 10 questions right, the teacher can convert 8/10 to a percent to give the student a grade.

When you're converting a percent into a fraction, it helps to remember that percents are always out of 100. You can practice with percents in our Introduction to Percentages lesson.

Click through the slideshow to learn how to convert a percent into a fraction.

Write these percentages as fractions. Make sure to **reduce** each fraction to its simplest form.

Converting a fraction uses two of the skills you just 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 fraction into a percent.

Click through the slideshow to learn how to convert a fraction into a percent.

Convert these fractions into percents.

Want even more practice? Try out a short assessment to test your skills by clicking the link below: