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Introduction

QUICK LINKS


Introduction

INTRO
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Think of fractions and decimals like Miles Morales and Spiderman. They're just two different representations of the same person.Fighting crime? Gotta go with Spiderman. Going to school? Probably need to stick with Miles.
Similarly, fractions and decimals can represent the same number, and we can think of long division as the transformation that takes us from a fraction to a decimal.
We can visualize fractions and decimals to see how equal pairs look the same:
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about converting fractions to decimals and test your understanding.

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CALCULATOR
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Fraction to Decimal Calculator


Step 1. Turn the fraction into a long division problem.

The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

Since the number inside is less than the number outside, add a decimal point and enough s to the end of the number inside to make it greater than or equal to the number outside.
On top, add followed by one fewer than what we added inside.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside (ignore the decimal) is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.
The remainder is , so we can stop. Our answer is .

Step 5. Add 0's

The remainder is now the new number we divide into, so we need it to be greater than or equal to the outside number.
We can add one for free, and then for every extra we add, we have to add one to the top, too.

Step 6. Repeat Steps 3-6 until the remainder is 0 or the decimal is long enough to use.

Once our remainder is , we can stop.
Our answer is .
KEY STEPS
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How to Convert Fractions to Decimals

Step 1. Turn the fraction into a long division problem.

The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

If the number inside is the number outside, add a decimal point and enough s to the end of the number inside to make it greater than or equal to the number outside.
On top, add followed by one fewer than what we added inside.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside (ignore the decimal) is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.
If the remainder is , you're done! Otherwise, continue to Step 5.

Step 5. Add 0's

The remainder is now the new number we divide into, so we need it to be greater than or equal to the outside number.
We can add one for free, and then for every extra we add, we have to add one to the top, too.

Step 6. Repeat Steps 3-6 until the remainder is 0 or the decimal is long enough to use.

The answer is the number on top, in this example, .
LESSON
β€” Converting Fractions to Decimals

Converting Fractions to Decimals

Because a fraction represents division, we can use long division to convert fractions to decimals.

For example, is like saying divided by . We can get the decimal result by doing the long division:
The answer on top is the decimal result equal to our fraction - in this case, it's .
Let’s walk through some example problems to see all the steps of long division!

EXAMPLE 1

Let's start by converting this fraction into a decimal:

Step 1. Turn the fraction into a long division problem.

The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

Since the number inside is less than the number outside, add a decimal point and enough s to the end of the number inside to make it greater than or equal to the number outside.
On top, add followed by one fewer than what we added inside.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside (ignore the decimal) is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.
The remainder is , so we can stop. Our answer is .

Step 5. Add 0's

The remainder is now the new number we divide into, so we need it to be greater than or equal to the outside number.
We can add one for free, and then for every extra we add, we have to add one to the top, too.

Step 6. Repeat Steps 3-6 until the remainder is 0 or the decimal is long enough to use.

Once our remainder is , we can stop.
Our answer is .

EXAMPLE 2

Nice work! Now, let's convert this fraction into a decimal:

Step 1. Turn the fraction into a long division problem.

The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

Since the number inside is bigger than the number outside, continue to Step 3.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.
The remainder is , so we can stop. Our answer is .

Step 5. Add 0's

First, we add a decimal point to the answer. The remainder is now the new number we divide into, so we need it to be greater than or equal to the outside number.
We can add one for free, and then for every extra we add, we have to add one to the top, too.

Step 6. Repeat Steps 3-6 until the remainder is 0 or the decimal is long enough to use.

Once our remainder is , we can stop.
Our answer is .

EXAMPLE 3

Amazing! Last problem - let's convert this fraction into a decimal:

Step 1. Turn the fraction into a long division problem.

Our fraction is negative, but we'll ignore that for now. The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

Since the number inside is less than the number outside, add a decimal point and enough s to the end of the number inside to make it greater than or equal to the number outside.
On top, add followed by one fewer than what we added inside.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside (ignore the decimal) is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.
The remainder is , so we can stop. And since our original fraction was negative, our decimal is negative as well. Our answer is .

Step 5. Add 0's

The remainder is now the new number we divide into, so we need it to be greater than or equal to the outside number.
We can add one for free, and then for every extra we add, we have to add one to the top, too.

Step 6. Repeat Steps 3-6 until the remainder is 0 or the decimal is long enough to use.

Once our remainder is , we can stop. And since our original fraction was negative, our decimal is negative as well.
Our answer is .
Awesome! If you’d like to practice additional problems converting fractions to decimals, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Converting Fractions to Decimals

Practice: Converting Fractions to Decimals

Question 1 of 10: Convert to a decimal.

Step 1. Turn the fraction into a long division problem.

The top number goes inside and the bottom number goes outside.

Step 2. Compare the size of the number inside to the size of the number outside.

Since the number inside is less than the number outside, add a decimal point and enough s to the end of the number inside to make it greater than or equal to the number outside.
On top, add followed by one fewer than what we added inside.

Step 3. Divide the number inside by the number outside.

The number of times the number outside goes into the number inside (ignore the decimal) is added to our answer in the top.

Step 4. Find the remainder.

Multiply the outside number by the number we just added to our answer, and subtract it from the number inside to get the remainder.

Nice work! Our remainder is 0, so we're done.
Our answer is the number on top: .
Great job! Our answer is

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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