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.

I got things wrong that I thought was right and I checked my work with a calculator, but Khan Academy still said I was wrong, and their answer was so confusing. 😭

I thought it was a waste of time trying to repeat the numbers a lot, but it really helps! Just try your best and remember not to leave a fraction with a decimal or the app will go NUTTS. I learned from experience.

I don't understand this at all please explain

It's okay that you don't understand it right away! Let me give you an example: write 0.6 repeating as a fraction. To begin the process, we set up an equation. x is equal to 0.666... x= 0.666 We are going to set up two equations, where we subtract the first equation (x= 0.666) from another equation, which we do not have yet. We want to set up the new equation so that, when we subtract our first equation (x = 0.666) from it, all numbers after the decimal place equal 0. This will give us a whole number. To do this, we need to move our decimal to the right. In some scenarios, this may involve multiplying by numbers like 100 or 1000. However, we only need to multiply by 10 here to move the decimal one place over to the right. Our new decimal would be: x= 6.666... But we're not done, whatever you do to one side of the equation, you have to do to the other. So.. 10x=6.666 Now we can take this new equation and subtract x=0.666 from it. 10x = 6.666 - x = 0.666 This gives us 9x=6. We now need to "solve" for x. So, we divide by 9 to get x= 6/9 The reason I put solve in quotation marks is because we already know what our x is! In this scenario, x equals 0.6 repeating. So 0.666 = 6/9 Finally, we simplify to get 0.666= 2/3 I always like to double check my answers, and luckily for us, these are very simple to double check. Simply punch 2 divided by 3 in your calculator, and you can verify that it equals 0.666. I hope this helped! :))

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.

i dont understand how you know what to multiply the decimal by its sometimes 10 100 1 1000 its so confusing

Ian's right. That's basically how you do it. But you can also use some other logic. It's kinda hard to explain in text. Maybe I'll try later because I'll have to go soon.

Main content

8th grade

Course: 8th grade > Unit 1

Lesson 1: Repeating decimals

Writing repeating decimals as fractions review

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...”
(32 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...”
  (52 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 ...”
(16 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...”
  (19 votes)
mackenziebowers
Posted 5 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...”
(19 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...”
  (8 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...”
(9 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...”
  (14 votes)
High Mage Duskpin
Posted 2 months ago. Direct link to High Mage Duskpin's post “I got things wrong that I...”
I got things wrong that I thought was right and I checked my work with a calculator, but Khan Academy still said I was wrong, and their answer was so confusing. 😭
Button navigates to signup pageComment on High Mage Duskpin's post “I got things wrong that I...”
(13 votes)
Answer
- tashahale328
  Posted a month ago. Direct link to tashahale328's post “I thought it was a waste ...”
  I thought it was a waste of time trying to repeat the numbers a lot, but it really helps! Just try your best and remember not to leave a fraction with a decimal or the app will go NUTTS. I learned from experience.
  Button navigates to signup page
  (7 votes)
I LOVE READING!!!!!
Posted 4 months ago. Direct link to I LOVE READING!!!!!'s post “I don't understand this a...”
I don't understand this at all please explain
Button navigates to signup pageComment on I LOVE READING!!!!!'s post “I don't understand this a...”
(11 votes)
Answer
- marshmallo
  Posted 4 months ago. Direct link to marshmallo's post “It's okay that you don't ...”
  It's okay that you don't understand it right away! Let me give you an example: write 0.6 repeating as a fraction.
  
  To begin the process, we set up an equation. x is equal to 0.666...
  
  x= 0.666
  
  We are going to set up two equations, where we subtract the first equation (x= 0.666) from another equation, which we do not have yet. We want to set up the new equation so that, when we subtract our first equation (x = 0.666) from it, all numbers after the decimal place equal 0. This will give us a whole number.
  
  To do this, we need to move our decimal to the right. In some scenarios, this may involve multiplying by numbers like 100 or 1000. However, we only need to multiply by 10 here to move the decimal one place over to the right. Our new decimal would be:
  
  x= 6.666...
  
  But we're not done, whatever you do to one side of the equation, you have to do to the other. So..
  
  10x=6.666
  
  Now we can take this new equation and subtract x=0.666 from it.
  
  10x = 6.666
  - x = 0.666
  
  This gives us 9x=6.
  
  We now need to "solve" for x. So, we divide by 9 to get
  
  x= 6/9
  
  The reason I put solve in quotation marks is because we already know what our x is! In this scenario, x equals 0.6 repeating. So
  
  0.666 = 6/9
  
  Finally, we simplify to get
  
  0.666= 2/3
  
  I always like to double check my answers, and luckily for us, these are very simple to double check. Simply punch 2 divided by 3 in your calculator, and you can verify that it equals 0.666.
  
  I hope this helped! :))
  Comment on marshmallo's post “It's okay that you don't ...”
  (11 votes)
sta3y
Posted 22 days ago. Direct link to sta3y's post “FOR EVERYONE WHO IS STRUG...”
FOR EVERYONE WHO IS STRUGGLING WITH THIS:

HERE'S HOW TO CONVERT REPEATING DECIMALS AS FRACTIONS.

Let's use 0.92222... (with the 2 repeating)

1) Since 2, the number being repeated is in the hundredth place, we move the decimal 2 places to the right. (or to the hundredth place) Doing that, we get 92.222222

2) Now the number we get from step 1 is labelled 100𝑥.
-> 100𝑥 = 92.22222

3) Let's find 10𝑥 now. This part is simple since it is simply repeating step #1 but with moving the decimal point only ONE space. So, 10𝑥 = 9.22222

4) Let's subtract 100𝑥 minus 10𝑥.
100𝑥 = 92.222
-10𝑥 = 9.222
-------------
90𝑥 = 83
= 83/90

A. Line up the numbers by the decimal point
B. Subtract 100𝑥 by 10𝑥 and 92.222 by 9.222
C. Divide the answer by 90𝑥 (put it in a fraction with 90 as the denominator)
D. That fraction is your answer! if it's an improper fraction (the numerator is larger than the denominator), you can turn it into a mixed fraction.

~~~~~~~~~~~~~~~~
I hope this helped anyone struggling with this topic! I'm not really sure if this was a good explanation but it's the best I can do :)

Don't give up if you don't get it the first time, it took me about 20 tries on the exercises to get 100%.
~~~~~~~~~
I'm willing to answer any questions so just reply to this comment and I'll try to get back to you!
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Answer
zaina.razak
Posted 2 months ago. Direct link to zaina.razak's post “i dont understand how you...”
i dont understand how you know what to multiply the decimal by its sometimes 10 100 1 1000 its so confusing
Button navigates to signup pageComment on zaina.razak's post “i dont understand how you...”
(9 votes)
Answer
- Kake
  Posted 2 months ago. Direct link to Kake's post “Ian's right. That's basic...”
  Ian's right. That's basically how you do it. But you can also use some other logic. It's kinda hard to explain in text. Maybe I'll try later because I'll have to go soon.
  Button navigates to signup page
  (6 votes)
Daniel Hametaj
Posted a year ago. Direct link to Daniel Hametaj's post “Why is math not fun?”
Why is math not fun?
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(10 votes)
Answer
- David Severin
  Posted a year 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...”
  (7 votes)
monrael27
Posted 2 years ago. Direct link to monrael27's post “hi how r u guys”
hi how r u guys
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(11 votes)
Answer
- koikoikoi74
  Posted 5 months ago. Direct link to koikoikoi74's post “im good hbu?”
  im good hbu?
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  (1 vote)