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!

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

start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54, end fraction, equals, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54

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

start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54, end fraction, equals, 0, point, 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:start fraction, 4, divided by, 9, end fraction

start fraction, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54, end fraction, equals, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54

\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.

start fraction, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54, end fraction, equals, 0, point, start overline, 4, end overline

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

Practice

Problem 1

Current

Select the decimal that is equivalent to start fraction, 2, divided by, 3, end fraction.

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!
  Comment on Ian Pulizzotto's post “Let x = 0.3666.... Only ...”
  (15 votes)
rusj5014
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