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## 8th grade

### Course: 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

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# 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:**$\frac{2}{5}$

## 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:**$\frac{4}{9}$

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(79 votes)
- "Want to try more problems like this?" Absolutively not(26 votes)
- UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating(9 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!(16 votes)

- why does the math have to be so hard(11 votes)
- Math makes life hard.(5 votes)

- i don't get none of this I think my brain don't care about math but i have to learn(13 votes)
- i was dying during this(9 votes)
- no because why was I struggling so much 💀💀(8 votes)
- 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.(2 votes)

- Thanks to Corona Virus, My teacher posted 402 assignments on here(7 votes)