why does math have to be hard like life is hard already

Math is the reason why life is hard to begin with lol

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.

at 5:31 how is the moon lartges enough to block the sun]

I think (don't quote me on this) it's because of how much closer it is to earth. There are a few planets between us and the sun, but the moon close enough for us to see it's craters. Hope this helps!!

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

$\begin{aligned} &~~ \, 0.{4} \\ \greenD5&\overline{\Big)\blueD2.0} \phantom{0000000}& \\ &\underline{\, \mbox{-}0}\,\,\,{\!\downarrow}&\\ &\phantom{0}{2\,\,0}& \\ &\underline{\, \mbox{-}2\,\,0}&\\ &\phantom{00}{\,\,0}&\\ \end{aligned}$

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

$\begin{aligned} &~~ \, 0.{4444} \\ \greenD9&\overline{\Big)\blueD4.0000} \phantom{0000000}& \\ &\underline{\, \mbox{-}0}\,\,\,{\!\downarrow}&\\ &\phantom{0}{4\,\,0}& \\ &\underline{\, \mbox{-}3\,\,6}{\,\,\!\downarrow}&&\\ &\phantom{00}{\,\,4\,0}&\\ &\underline{\,\,\,\,\,\, \mbox{-}3\,6}{\,\,\!\downarrow}\,\,\\\ &\phantom{0000}{4\,0}& \\ &\underline{\,\,\,\,\,\,\,\,\,\, \mbox{-}3\,6}&\\ &\phantom{000\,\,0}{\,\,4}&\\ \end{aligned}$

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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hs1689589
Posted 8 months ago. Direct link to hs1689589's post “why does math have to be ...”
why does math have to be hard like life is hard already
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(58 votes)
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- ellaerogers21
  Posted 6 months ago. Direct link to ellaerogers21's post “Math is the reason why li...”
  Math is the reason why life is hard to begin with lol
  Comment on ellaerogers21's post “Math is the reason why li...”
  (22 votes)
Mohak Upmanyue
Posted 2 years ago. Direct link to Mohak Upmanyue's post “UH I am still a bit confu...”
UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating
Button navigates to signup pageComment on Mohak Upmanyue's post “UH I am still a bit confu...”
(7 votes)
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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 ...”
  (16 votes)
rusj5014
Posted 8 months ago. Direct link to rusj5014's post “why does the math have to...”
why does the math have to be so hard
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- I'm1Loser
  Posted 4 months ago. Direct link to I'm1Loser's post “Math makes life hard.”
  Math makes life hard.
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Thanks to Corona Virus, My teacher posted 402 assignments on here
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  i now right
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my car handle hit the car door
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Nickname
Posted a year ago. Direct link to Nickname's post “I am a bit confused when ...”
I am a bit confused when 2 numbers repeat, when I do it it sometimes work and sometimes not… idk
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(6 votes)
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- David Severin
  Posted a year 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.
  Comment on David Severin's post “The key is to multiply by...”
  (3 votes)
xavier
Posted 4 years ago. Direct link to xavier's post “why didn't the video expl...”
why didn't the video explain how to do the problems with 2 behind the decimal and 1 decimal repeating
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mikeblack3rd
Posted 5 months ago. Direct link to mikeblack3rd's post “i am a 7 yr old”
i am a 7 yr old
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Andrew
Posted 7 months ago. Direct link to Andrew's post “at 5:31 how is the moon l...”
at
5:31
how is the moon lartges enough to block the sun]
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- ellaerogers21
  Posted 6 months ago. Direct link to ellaerogers21's post “I think (don't quote me o...”
  I think (don't quote me on this) it's because of how much closer it is to earth. There are a few planets between us and the sun, but the moon close enough for us to see it's craters. Hope this helps!!
  Comment on ellaerogers21's post “I think (don't quote me o...”
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lwoods
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why does quick sand move slowly
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