Converting fractions, decimals, and percents

When we talk, we regularly use different words to express the very same thing. Because that example, we could describe the same auto as tiny or little or small. Every one of these words typical the vehicle is not big. Fractions, decimals, and percents are favor the native tiny, little, and also small. They're every just different ways of to express parts of a whole.

You are watching: 85 as a fraction in simplest form


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In this image, every measuring cup has the very same amount the juice in it. However we've to express this quantity in 3 ways: as a fraction, as a percent, and also as a decimal. Due to the fact that they're express the very same amount, we recognize that 1/2, 50%, and 0.5 are equal to each other. Any time we see 1/2, we'll understand it can also mean 50% or 0.5.

Sometimes it's helpful to convert one kind of number right into another. For example, it's much easier to include 1/4 and 0.5 if you revolve 0.5 into a fraction. Learning just how to transform fractions, decimals, and percents will certainly also assist you together you learn much more advanced math.

Fractions and also decimals

Every portion can additionally be written as a decimal, and also vice versa. You might not carry out this an extremely often, however converting decimals and fractions can aid you in math. For example, it's less complicated to subtract 1/6 from 0.52 if you turn 1/6 into a decimal first.

Converting a portion into a decimal

Let's convert a fraction into a decimal. We'll be utilizing a math ability you've currently learned: long division. To refresh your memory ~ above this skill, you deserve to review ours Long division lesson.

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

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

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To convert a portion into a decimal, we'll just divide the numerator...

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

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In ours example, we'll divide 1 through 4.

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1 split by 4 amounts to 0.

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To store dividing, we'll include a decimal point and also a zero after the 1.

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

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Now we deserve to divide 10 by 4.

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10 split by 4 amounts to 2.

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Now we'll main point 4 through 2.

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4 times 2 amounts to 8. For this reason we'll subtract 8 native 10.

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10 minus 8 equals 2.

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Since 2 is better than 0, we're no finished separating yet. We'll add another 0 after the decimal allude and bring it down.

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Now we'll divide 20 by 4.

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20 separated by 4 equals 5.

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

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When we subtract 20 from 20, we acquire 0. The 0 method we're done dividing.

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1 separated by 4 amounts to 0.25.

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So 1/4 is same to 0.25.

Try This!

Convert every of these fractions right into a decimal.


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Converting a decimal into a fraction

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

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

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We're going come rewrite 0.85 as a fraction. To transform a decimal right into a fraction, we'll usage place values.

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In decimals, the number automatically to the ideal of the decimal suggest is in the tenths place.

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The ar to the right of the tenths location is the hundredths place.

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To transform a decimal, an initial we'll examine the place value the the last number come the right.

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In 0.85, 5 is in the hundredths place.

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This way our decimal is equal to 85 hundredths. 85 hundredths can additionally be written as 85/100.

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Now we have our fraction. However it's constantly a an excellent idea come ryellowcomic.comce fractions once we can—it renders them simpler to read.

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To ryellowcomic.comce, we need to uncover the largest number that will go evenly right into both 85 and 100.

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5 is the biggest number that goes evenly right into 85 and 100. For this reason we'll division both parts of our fraction by 5.

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First we'll division the numerator. 85 split by 5 amounts to 17.

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Now we'll divide the denominator. 100 divided by 5 amounts to 20. This means 85/100 have the right to be ryellowcomic.comced come 17/20.

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So 0.85 is same to 17/20.

Ryellowcomic.comcing a fraction may it seems to be ~ unnecessary as soon as you're converting a decimal. However it's essential if you're walking to usage the fraction in a math problem. If you're adding 2 fractions, you may also need to ryellowcomic.comce or change both fractions so they have a common denominator.

Try This!

Convert these decimals into fractions. Be certain to ryellowcomic.comce each portion to its easiest form!


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Percents and decimals

Knowing just how to convert percents and also decimals will aid you calculation things choose sales tax and also discounts. To discover how, inspect out our Percentages in genuine Life lesson.

Converting a percent right into a decimal

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

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

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We're walking to convert 17% right into a decimal.

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

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

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Next, we'll move the decimal point two spaces to the left.

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Now we'll move the decimal allude two spaces come the left.

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

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Let's watch at one more example. This time we'll turn 78% into a decimal.

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

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

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

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78% is same to 0.78.

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

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First, we'll change the percent sign v a decimal point.

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

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

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

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

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8% is same to .08

Why go this work?

Converting percents into decimals is so simple that you might feel prefer you've let go something. Yet don't worry—it really is the simple! Here's why the an approach we proved you works.

When we rotate a percent right into a decimal, we're in reality doing 2 steps. First, we transform our percent right into a fraction. Because all percents room out the 100, we simply put the percent over 100, choose this:

78% = 78/100

In the 2nd step, we transform 78/100 into a decimal. You already know this way we'll division the numerator through the denominator, favor this:

78 ÷ 100 = 0.78

So why didn't we show you these steps in the slideshow? due to the fact that you can get the answer without them. You understand that all percents room out that 100, therefore you deserve to skip do the percent right into a fraction. You need to divide the percent by 100 to obtain a decimal, yet there's a quick way to do that. Simply move the decimal point two spaces come the left! This way, friend can get the same answer with just one basic step.

Try This!

Convert these percents into decimals.


Converting a decimal right into a percent

Now we'll reverse what you simply learned. Let's transform a decimal into a percent.

Click with the slideshow come see just how to transform a decimal right into a percent.

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We're walk to convert 0.45 right into a percent.

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We'll reverse what we did in the last section. This time, we'll relocate the decimal suggest two places to the right.

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We'll reverse what us did in the last section. This time, we'll move the decimal suggest two areas to the right.

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Now we'll change the decimal allude with a percent sign.

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We've perfect converting our decimal into a percent. 0.45 is equal to 45%.

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

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But we're quiet going to move the decimal point two spaces come the right.

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

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

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Instead, we'll keep the decimal suggest and add a percent authorize at the end of the number.

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So 0.635 is equal to 63.5%.

Try This!

Calculate this decimals as percents.


Percents and also fractions

Knowing how to create percents as fractions and also vice versa can help you in your day-to-day life. For example, let's say you earn a grade of 80% top top a test. Friend can transform 80% right into a fraction to find out how many of your answers were correct. When your teacher qualities the test, she may do the opposite. If a student got 8 out of 10 inquiries right, the teacher can convert 8/10 come a percent to offer the student a grade.

Converting a percent right into a fraction

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

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

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We're walking to convert 30% right into a fraction.

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

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Now we've convert 30% into a fraction, yet we still have to ryellowcomic.comce it.

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

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We'll division the numerator of the fraction first. 30 divided by 10 amounts to 3.

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Now we'll divide the denominator. 100 split by 10 equals 10.

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So 30% is same to 3/10.

Try This!

Write these percentages as fractions. Make certain to ryellowcomic.comce each fraction to its easiest form.


Converting a portion into a percent

Converting a fraction uses 2 of the an abilities you just learned: creating a fraction as a decimal, and also writing a decimal together a percent. Let's see exactly how we deserve to use these an abilities to transform a portion into a percent.

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

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Let's convert 3/6 into a percent.

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Just like as soon as we converted a fraction into a decimal, we'll divide the numerator by the denominator.

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3 split by 6 amounts to 0.5.

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We've turn our portion into a decimal.

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Now we'll rotate the decimal right into a percent by relocating the decimal allude two spaces come the right.

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

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