Main content

## 8th grade

### Unit 1: Lesson 1

Repeating decimals- Converting a fraction to a repeating decimal
- Writing fractions as repeating decimals
- Converting repeating decimals to fractions (part 1 of 2)
- Converting repeating decimals to fractions
- Converting repeating decimals to fractions (part 2 of 2)
- Converting multi-digit repeating decimals to fractions
- Writing repeating decimals as fractions review
- Writing fractions as repeating decimals review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Writing fractions as repeating decimals review

Review converting fractions to repeating decimals, and then try some practice problems.

## Writing fractions as decimals

To convert a fraction to a decimal, we divide the numerator by the denominator.

**Example:start fraction, 2, divided by, 5, end fraction**

## Writing fractions as repeating decimals

However, it does not always work out that nicely.

Sometimes, when we divide the numerator by the denominator, it becomes clear that the digits will keep repeating. In this case, we write the answer as a repeating decimal.

In our answer, we write a bar over the repeating digits to show that they repeat.

**Example:start fraction, 4, divided by, 9, end fraction**

No matter how long we divide, the 4 will continue to repeat in our quotient.

*Want to learn more about writing fractions as repeating decimals? Check out this video.*

## Want to join the conversation?

- why does math have to be hard like life is hard already(38 votes)
- Math is the reason why life is hard to begin with lol(7 votes)

- UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating(7 votes)
- Let x = 0.3666....

Only 1 digit (the 6) repeats, so multiply both sides by 10^1=10 to get

10x = 3.6666...

Subtract the first equation from the second equation to cancel out repeating parts, to get

9x = 3.3

Divide both sides by 9 to get

x = 3.3/9 .

We can simplify 3.3/9 by first multiplying top and bottom by 10 (getting rid of the decimal) to get 33/90, then dividing top and bottom by 3 to get 11/30.

The final answer is 11/30.

Have a blessed, wonderful day!(7 votes)

- why does the math have to be so hard(8 votes)
- Math makes life hard.(1 vote)

- I am a bit confused when 2 numbers repeat, when I do it it sometimes work and sometimes not… idk(6 votes)
- The key is to multiply by a power of 10 equal to the number of repeating decimals. If you have two numbers repeating, you have to multiply by 100. Example: what is x=.353535... as a fraction? Multiply by 100 to get 100x = 35.353535..., then when you subtract, you get 99x=35, so x = 35/99. If you notice, if it is only repeating numbers, the repeating part will be divided by some number of 9s. .444... = 4/9. .464646... = 46/99, .456456456... = 456/999. .456745674567... = 4567/9999.(1 vote)

- Thanks to Corona Virus, My teacher posted 402 assignments on here(5 votes)
- why didn't the video explain how to do the problems with 2 behind the decimal and 1 decimal repeating(4 votes)
- at5:31how is the moon lartges enough to block the sun](3 votes)
- I think (don't quote me on this) it's because of how much closer it is to earth. There are a few planets between us and the sun, but the moon close enough for us to see it's craters. Hope this helps!!(2 votes)

- my car handle hit the car door(3 votes)
- door car the hit handle car my(1 vote)

- is there anything on transformations of a line to a another line on a graph from stuff like f(x) to g(x) on here. If so plz tell me.(3 votes)
- how to simplify fractions(2 votes)
- First, find the GCF (greatest common factor). To do this, prime factorize both numbers and choose the largest factors they both have. Multiply these factors, and you have th GCF. Divide both the numerator and denominator by this number, and you have the fraction in simplest form.(2 votes)