UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating

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!

I am a bit confused when 2 numbers repeat, when I do it it sometimes work and sometimes not… idk

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.

Main content

8th grade

Course: 8th grade > Unit 1

Lesson 1: Repeating decimals

Writing fractions as repeating decimals review

Google Classroom

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: $\frac{2}{5}$ ‍

\frac{2}{5} = 2 \div 5

\begin{aligned} 0. 4 \\ 5 & \overset{―}{) 2 .0} \\ \underset{―}{- 0} ↓ \\ 2 0 \\ \underset{―}{- 2 0} \\ 0 \end{aligned}

\frac{2}{5} = 0.4

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: $\frac{4}{9}$ ‍

\frac{4}{9} = 4 \div 9

\begin{aligned} 0. 4444 \\ 9 & \overset{―}{) 4 .0000} \\ \underset{―}{- 0} ↓ \\ 4 0 \\ \underset{―}{- 3 6} ↓ \\ 4 0 \\ \underset{―}{- 3 6} ↓ \\ 4 0 \\ \underset{―}{- 3 6} \\ 4 \end{aligned}

No matter how long we divide, the

4

will continue to repeat in our quotient.

\frac{4}{9} = 0. \overset{―}{4}

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

Practice

Problem 1

Select the decimal that is equivalent to $\frac{2}{3}$ ‍.

Want to try more problems like this? Check out this exercise.

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UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating
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- Ian Pulizzotto
  Posted 2 years ago. Direct link to Ian Pulizzotto's post “Let x = 0.3666.... Only ...”
  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!
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rusj5014
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I am a bit confused when 2 numbers repeat, when I do it it sometimes work and sometimes not… idk
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- David Severin
  Posted 2 years ago. Direct link to David Severin's post “The key is to multiply by...”
  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.
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