What is 0.78 with the 8 repeating?

First, you want to create two equations where the repeating digit (in this case the 8) is alone on the right side of the decimal point. So for the first equation, multiply both sides by ten, to get: 10x = 7.888... For the second, multiply both sides by 100, to get a different equation with the same repeating eight on the right side of the decimal point: 100x = 78.888... Then subtract the two equations. It helps to see them together: 100x = 78.888... 10x = 7.888... The repeating 8 is subtracted out, to get: 90x = 71 Divide both sides by 90: x = 71/90 71/90 is fully reduced, so that's the answer. I hope that helps!

How do we repeating decimals to fractions? I have a problem find the repeating decimal to a fractions?

Converting repeating decimals to fractions Let x equal the repeating decimal you are trying to convert to a fraction. Examine the repeating decimal to find the repeating digit(s). Place the repeating digit(s) to the left of the decimal point. Place the repeating digit(s) to the right of the decimal point.

what could you do if you had 0.2 repted

if it is just one integer that is repeating, such as .1111 or .2222, it is that integer over 9. .1111=1/9, etc.

Well my mom kicked me out of the housevso NJ sure itvgraet

The correct question is why is math not fun for me? (me meaning you). Math is fun for me because I have good number sense.

what does the little line at the top of the number mean

In a decimal number, a bar over. In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end.

how would I simplify a repeating decimal like 0.63636363...?

Let x = 0.63636363... Two digits (63) repeat, so multiply both sides by 10^2=100 to get 100x = 63.636363... Subtracting the first equation from the second equation accomplishes the main goal of canceling out the repeating part: 99x = 63. Dividing both sides by 99 gives x = 63/99 = 7/11. So 0.63636363... converts to 7/11.

is 8th grade math use in college?

Although you probably wouldn't learn 8th Grade Math in college, it is used a building block for the actual math you would learn in college.

How would I turn 1.83333... into a simplified fraction?

The first step is to turn it into two equations with the same decimal. So here, to get only the 3 repeating to the right of the decimal point, the first equation would be multiplied by 10, to make: 10x = 18.333... For the second equation, multiplying it by 100 makes sense, to create a different equation. Therefore: 100x = 183.333... Subtract the two equations from each other. Setting it up like this visually makes more sense to me, at least: 100x = 183.333... 10x = 18.333... The decimal cancels, so it comes out to: 90x = 165 Divide both sides by 90 to make it equal to x: x = 165/90 Simplify the fraction by dividing out 15: x = 11/6 I hope that makes sense!

Main content

8th grade

Course: 8th grade > Unit 1

Lesson 1: Repeating decimals

Writing repeating decimals as fractions review

CCSS.Math:

8.NS.A.1

Google Classroom

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

Writing decimals as fractions

To convert a decimal to a fraction, we write the decimal number as a numerator, and we write its place value as the denominator.

Example 1: 0, point, 07

0, point, 0, start color #11accd, 7, end color #11accd is start color #11accd, 7, end color #11accd start text, start color #1fab54, h, u, n, d, r, e, d, t, h, s, end color #1fab54, end text. So, we write start color #11accd, 7, end color #11accd over start color #1fab54, 100, end color #1fab54.

0, point, 07, equals, start fraction, start color #11accd, 7, end color #11accd, divided by, start color #1fab54, 100, end color #1fab54, end fraction

But what about repeating decimals?

Let's look at an example.

Rewrite 0, point, start overline, 7, end overline as a simplified fraction.

Let x equal the decimal:

x, equals, 0, point, 7777, point, point, point

Set up a second equation such that the digits after the decimal point are identical:

$\large{\begin{aligned} 10x &= 7.7777...\\ x &= 0.7777... \end{aligned}}$

Subtract the two equations:

9, x, equals, 7

Solve for x:

x, equals, start fraction, 7, divided by, 9, end fraction

Remember from the first step that x is equal to our repeating decimal, so:

0, point, start overline, 7, end overline, equals, start fraction, 7, divided by, 9, end fraction

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

Practice

Problem 1

Current

Rewrite as a simplified fraction.

0, point, start overline, 2, end overline, equals, question mark

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

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$hopper cool style avatar for user \«π$
\«π
Posted 6 years ago. Direct link to \«π's post “What is 0.78 with the 8 r...”
What is 0.78 with the 8 repeating?
Button navigates to signup pageComment on \«π's post “What is 0.78 with the 8 r...”
(27 votes)
Answer
- Quatania
  Posted 2 years ago. Direct link to Quatania's post “First, you want to create...”
  First, you want to create two equations where the repeating digit (in this case the 8) is alone on the right side of the decimal point.
  
  So for the first equation, multiply both sides by ten, to get:
  
  10x = 7.888...
  
  For the second, multiply both sides by 100, to get a different equation with the same repeating eight on the right side of the decimal point:
  
  100x = 78.888...
  
  Then subtract the two equations. It helps to see them together:
  
  100x = 78.888...
  10x = 7.888...
  
  The repeating 8 is subtracted out, to get:
  
  90x = 71
  
  Divide both sides by 90:
  
  x = 71/90
  
  71/90 is fully reduced, so that's the answer.
  
  I hope that helps!
  Comment on Quatania's post “First, you want to create...”
  (45 votes)
abbi.campbell
Posted 5 years ago. Direct link to abbi.campbell's post “what could you do if you ...”
what could you do if you had 0.2 repted
Button navigates to signup pageComment on abbi.campbell's post “what could you do if you ...”
(15 votes)
Answer
- ogjoni
  Posted 3 years ago. Direct link to ogjoni's post “if it is just one integer...”
  if it is just one integer that is repeating, such as .1111 or .2222, it is that integer over 9. .1111=1/9, etc.
  Comment on ogjoni's post “if it is just one integer...”
  (17 votes)
mackenziebowers
Posted 4 years ago. Direct link to mackenziebowers's post “How do we repeating decim...”
How do we repeating decimals to fractions? I have a problem find the repeating decimal to a fractions?
Button navigates to signup pageComment on mackenziebowers's post “How do we repeating decim...”
(16 votes)
Answer
- Joann
  Posted 3 years ago. Direct link to Joann's post “Converting repeating deci...”
  Converting repeating decimals to fractions
  Let x equal the repeating decimal you are trying to convert to a fraction.
  Examine the repeating decimal to find the repeating digit(s).
  Place the repeating digit(s) to the left of the decimal point.
  Place the repeating digit(s) to the right of the decimal point.
  Comment on Joann's post “Converting repeating deci...”
  (6 votes)
Dalton Wayne Moore #22
Posted 3 years ago. Direct link to Dalton Wayne Moore #22's post “what does the little line...”
what does the little line at the top of the number mean
Button navigates to signup pageComment on Dalton Wayne Moore #22's post “what does the little line...”
(7 votes)
Answer
- Joann
  Posted 3 years ago. Direct link to Joann's post “In a decimal number, a ba...”
  In a decimal number, a bar over. In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end.
  Comment on Joann's post “In a decimal number, a ba...”
  (12 votes)
Daniel Hametaj
Posted 10 months ago. Direct link to Daniel Hametaj's post “Why is math not fun?”
Why is math not fun?
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(9 votes)
Answer
- David Severin
  Posted 10 months ago. Direct link to David Severin's post “The correct question is w...”
  The correct question is why is math not fun for me? (me meaning you). Math is fun for me because I have good number sense.
  Comment on David Severin's post “The correct question is w...”
  (5 votes)
monrael27
Posted a year ago. Direct link to monrael27's post “hi how r u guys”
hi how r u guys
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(10 votes)
Answer
- Olivia McIntosh
  Posted 2 months ago. Direct link to Olivia McIntosh's post “Well my mom kicked me out...”
  Well my mom kicked me out of the housevso NJ sure itvgraet
  Comment on Olivia McIntosh's post “Well my mom kicked me out...”
  (3 votes)
boopleshmoop
Posted 3 years ago. Direct link to boopleshmoop's post “how would I simplify a re...”
how would I simplify a repeating decimal like 0.63636363...?
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(6 votes)
Answer
- Ian Pulizzotto
  Posted 3 years ago. Direct link to Ian Pulizzotto's post “Let x = 0.63636363... T...”
  Let x = 0.63636363...
  
  Two digits (63) repeat, so multiply both sides by 10^2=100 to get
  100x = 63.636363...
  
  Subtracting the first equation from the second equation accomplishes the main goal of canceling out the repeating part:
  99x = 63.
  
  Dividing both sides by 99 gives
  x = 63/99 = 7/11.
  
  So 0.63636363... converts to 7/11.
  Comment on Ian Pulizzotto's post “Let x = 0.63636363... T...”
  (7 votes)
that one kid
Posted a year ago. Direct link to that one kid's post “is 8th grade math use in ...”
is 8th grade math use in college?
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(4 votes)
Answer
- Neal
  Posted a year ago. Direct link to Neal's post “Although you probably wou...”
  Although you probably wouldn't learn 8th Grade Math in college, it is used a building block for the actual math you would learn in college.
  Button navigates to signup page
  (8 votes)
diyanampy
Posted 2 years ago. Direct link to diyanampy's post “How would I turn 1.83333....”
How would I turn 1.83333... into a simplified fraction?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Quatania
  Posted 2 years ago. Direct link to Quatania's post “The first step is to turn...”
  The first step is to turn it into two equations with the same decimal.
  
  So here, to get only the 3 repeating to the right of the decimal point, the first equation would be multiplied by 10, to make:
  
  10x = 18.333...
  
  For the second equation, multiplying it by 100 makes sense, to create a different equation. Therefore:
  
  100x = 183.333...
  
  Subtract the two equations from each other. Setting it up like this visually makes more sense to me, at least:
  
  100x = 183.333...
  10x = 18.333...
  
  The decimal cancels, so it comes out to:
  
  90x = 165
  
  Divide both sides by 90 to make it equal to x:
  
  x = 165/90
  
  Simplify the fraction by dividing out 15:
  
  x = 11/6
  
  I hope that makes sense!
  Comment on Quatania's post “The first step is to turn...”
  (11 votes)
Mackenzie448
Posted 3 years ago. Direct link to Mackenzie448's post “this is so confusing take...”
this is so confusing take me back to school at this point.
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(7 votes)
Answer
- Julie Rush
  Posted 6 months ago. Direct link to Julie Rush's post “its not confusing once yo...”
  its not confusing once you know what your doing.
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  (0 votes)