### Converting fractions, decimals, and also percents

When we talk, we frequently use different words come express the same thing. Because that example, we could describe the same car as **tiny** or **little** or **small**. Every one of these words median the car is not big. Fractions, decimals, and percents are like the words **tiny**, **little**, and **small**. They're every just various ways of express **parts** that a **whole**.

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

Sometimes it's valuable to convert one type of number into another. For example, it's much simpler to include 1/4 and 0.5 if you turn 0.5 into a fraction. Learning exactly how to convert fractions, decimals, and percents will certainly also assist you together you learn much more advanced math.

### Fractions and also decimals

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

Converting a portion into a decimalLet's convert a portion into a decimal. We'll be making use of a math skill you've already learned: long division. Come refresh her memory on this skill, you deserve to review our Long division lesson.

Click v the slideshow to learn just how to transform a portion into a decimal.

Let's see how we can transform 1/4 into a decimal.

To transform a fraction into a decimal, we'll simply divide the numerator...

To convert a portion to a decimal, we'll simply divide the numerator...by the denominator.

In ours example, we'll division 1 by 4.

1 separated by 4 equates to 0.

To keep dividing, we'll add a **decimal point** and a **zero** after the 1.

We'll also add a decimal suggest after the 0 on top.

Now we deserve to divide 10 by 4.

10 split by 4 equates to 2.

Now we'll main point 4 through 2.

4 time 2 equals 8. So we'll subtract 8 indigenous 10.

10 minus 8 equals 2.

Since 2 is higher than 0, we're no finished dividing yet. We'll add another 0 ~ the decimal suggest and bring it down.

Now we'll division 20 through 4.

20 divided by 4 amounts to 5.

Now we'll multiply. 4 times 5 equates to 20.

When we subtract 20 native 20, we obtain 0. The 0 method we're done dividing.

1 split by 4 amounts to 0.25.

So 1/4 is same to 0.25.

Try This!Convert every of these fractions into a **decimal**.

Converting a decimal into a fraction

Now we'll carry out it in reverse. Let's convert a decimal into a fraction.

Click with the slideshow to see exactly how to convert a decimal right into a fraction.

We're going to rewrite 0.85 together a fraction. To transform a decimal right into a fraction, we'll use **place values**.

In decimals, the number instantly to the best of the decimal point is in the **tenths** place.

The location to the ideal of the tenths place is the **hundredths place**.

To transform a decimal, first we'll inspect the location value that the last number to the right.

In 0.85, 5 is in the percentage percent place.

This way our decimal is same to 85 hundredths. 85 hundredths can also be written as 85/100.

Now we have our fraction. But it's always a great idea to alleviate fractions as soon as we can—it makes them simpler to read.

To rdearteassociazione.orgce, we require to uncover the biggest number that will certainly go evenly into both 85 and 100.

5 is the largest number that goes evenly into 85 and 100. So we'll division both components of our portion by 5.

First we'll divide the numerator. 85 separated by 5 equals 17.

Now we'll division the denominator. 100 separated by 5 amounts to 20. This way 85/100 deserve to be lessened to 17/20.

So 0.85 is same to 17/20.

Rdearteassociazione.orgcing a portion may it seems to be ~ unnecessary as soon as you're converting a decimal. But it's necessary if you're going to use the portion in a math problem. If you're **adding** 2 fractions, you may even need come **rdearteassociazione.orgce** or **change** both fountain so they have a **common denominator**.

Convert this decimals right into fractions. Be sure to **rdearteassociazione.orgce** each portion to its easiest form!

### Percents and decimals

Knowing exactly how to convert percents and also decimals will aid you calculate things choose sales tax and discounts. To discover how, inspect out ours Percentages in actual Life lesson.

Converting a percent right into a decimalConverting a percent right into a decimal is how amazing easy. It just takes a few simple steps.

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

We're going to transform 17% right into a decimal.

First, we'll take the percent sign...

First, we'll take it the percent sign...and revolve it into a decimal point.

Next, we'll relocate the decimal suggest **two** spaces to the **left**.

Now we'll relocate the decimal point **two** spaces come the **left**.

We've convert our percent come a decimal. 17% is equal to 0.17.

Let's watch at an additional example. This time we'll revolve 78% right into a decimal.

First, we'll replace the **percent sign** through a **decimal point**.

Then we'll relocate the decimal point **two** spaces come the **left**.

Then we'll relocate the decimal point **two** spaces come the **left**.

78% is same to 0.78.

Let's look at at another example. This time we'll rotate 8% right into a decimal.

First, we'll replace the **percent sign** through a **decimal point**.

Then, we'll move the decimal suggest **two** spaces come the **left**.

Then, we'll move the decimal point **two** spaces come the **left**.

Notice over there is an extra room next to the 8. Us can't simply leave an open space with nothing in it. Due to the fact that zero equals nothing, we'll change the an are with **zero**.

Notice there is an extra space next come the 8. We can't just leave an open an are with nothing in it. Due to the fact that zero equals nothing, we'll replace the space with **zero**.

8% is same to .08

Why walk this work?Converting percents right into decimals is so easy that you may feel prefer you've missed something. However don't worry—it really is that simple! Here's why the technique we verified you works.

When we revolve a percent right into a decimal, we're actually doing two steps. First, we convert our percent into a fraction. Due to the fact that all percents are out the 100, we just put the percent over 100, choose this:

78% = 78/100

In the 2nd step, we transform 78/100 right into a decimal. You already know this method we'll divide the **numerator** by the **denominator**, like this:

78 ÷ 100 = 0.78

So why didn't we display you these measures in the slideshow? because you can gain the answer there is no them. You know that every percents are out that 100, therefore you can skip making the percent right into a fraction. You have to divide the percent through 100 to acquire a decimal, yet there's a quick way to do that. Simply move the decimal allude two spaces to the left! This way, you can gain the same answer with simply one easy step.

Try This!Convert these percents right into decimals.

Converting a decimal right into a percent

Now we'll turning back what you simply learned. Let's convert a decimal into a percent.

Click v the slideshow to see exactly how to transform a decimal into a percent.

We're going to convert 0.45 into a percent.

We'll turning back what we did in the critical section. This time, we'll relocate the decimal suggest two places to the **right**.

We'll turning back what us did in the critical section. This time, we'll relocate the decimal point two locations to the **right**.

Now we'll replace the decimal suggest with a percent sign.

We've finished converting ours decimal right into a percent. 0.45 is equal to 45%.

Let's shot another example. This time our decimal has actually **three** numbers to the ideal of the decimal point.

But we're still going to move the decimal point **two** spaces to the right.

But we're tho going to relocate the decimal point **two** spaces come the right.

We still have actually a number to the **right** of the decimal point. The number **isn't** a 0, so we can't fall it.

Instead, we'll **keep** the decimal allude and **add** a percent sign at the end of the number.

So 0.635 is same to 63.5%.

Try This!Calculate these decimals as percents.

### Percents and fractions

Knowing how to write percents together fractions and also vice versa can assist you in your everyday life. Because that example, let's say you earn a great of 80% ~ above a test. Girlfriend can convert 80% right into a fraction to uncover out how numerous of her answers were correct. As soon as your teacher qualities the test, she may do the opposite. If a student gained 8 out of 10 concerns right, the teacher can convert 8/10 to a percent to offer the student a grade.

Converting a percent into a fractionWhen you're convert a percent into a fraction, it help to remember that percents are constantly out the 100. You deserve to practice through percents in our introduction to Percentages lesson.

Click v the slideshow come learn exactly how to transform a percent right into a fraction.

We're walk to transform 30% into a fraction.

So any type of percent is same to itself end 100. In ours example, 30% is same to 30/100.

Now we've converted 30% into a fraction, but we still require to alleviate it.

10 is the biggest number the goes evenly right into 30 and 100. For this reason we can divide both components of the fraction by 10.

We'll division the molecule of the fraction first. 30 divided by 10 equates to 3.

Now we'll divide the denominator. 100 divided by 10 amounts to 10.

So 30% is equal to 3/10.

Try This!Write these percentages as fractions. Make certain to **rdearteassociazione.orgce** each portion to its most basic form.

Converting a portion into a percent

Converting a fraction uses two of the an abilities you simply learned: creating a **fraction together a decimal**, and writing a **decimal together a percent**. Let's see just how we deserve to use these an abilities to transform a fraction into a percent.

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

Let's convert 3/6 into a percent.

Just like as soon as we converted a portion into a decimal, we'll division the **numerator** by the **denominator**.

3 separated by 6 equates to 0.5.

We've turned our fraction into a decimal.

Now we'll turn the decimal into a percent by moving the decimal suggest two spaces come the right.

Now we'll revolve the decimal into a percent by moving the decimal point two spaces to the right.

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We'll also change the decimal suggest into a percent sign. 0.50 is same to 50%.