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# Converting repeating decimals to fractions (part 2 of 2)

Learn how to convert the repeating decimals 0.363636... and 0.714141414... and 3.257257257... to fractions. Created by Sal Khan.

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• what is 0.333333333333333 in a fraction
• Here's a little table of repeating decimals. Notice that they all follow a pattern:

1/9 = 0.111111111111111...
2/9 = 0.222222222222222...
3/9 = 0.333333333333333...
4/9 = 0.444444444444444...
5/9 = 0.555555555555555...
6/9 = 0.666666666666666...
7/9 = 0.777777777777777...
8/9 = 0.888888888888888...

Because 3/9 = 1/3 and 6/9 = 2/3, the following are also true:

1/3 = 3/9
1/3 = 0.333333333333333...

2/3 = 6/9
2/3 = 0.666666666666666...

Hope this helps!
• Why would the repeating decimal 0.714141414... which equals x be multiplied by 100 instead of 1000 or 10?
• so you will have 71 left over and you will get rid of the other numbers that are after the decimal.
• okk but how do I solve the repeated beatings I get for not getting all A's
• How do you know when to multiply them by 1000x and 10x or 100x and 1x?
• If there are 2 digits that are behind the decimal point, it is 100x (or whatever variable you want to use.) If there are 3 digits that are behind the decimal point, it is 1000x. You can see that depending on the number of digits that are behind the decimal point, the same number of zeros trail along. 2 digits behind the decimal point are 100x You can see that 100 has 2 zeros. So depending on the number of digits that are behind the decimal point, that's how many zeros are gonna be trailing 1. 4 digits that are behind the decimal point are going to be 10000x as there are 4 zeros in 10000. You can see what you should do now.
• why is this so hard
• You might think it is hard, but once you keep training, and it's stuck like super glue to your brain, you will think it's super easy!
• and what if you had for example 2.717 with 717 reapeating how does that work
• Pretty much the same as in the video. If the 717 is repeating, then that's a period of 3 digits. To get rid of 3 digits, we multiply by 1000 (10^3), and subtract the original number:
1000x - x = 2717.717717717... - 2.717717717...
If you line those up as in the video, you'll see that the repeating numbers cancel out, and we get:
999x = 2715
Divide both sides by 999:
x = 2715 / 999
2.717717... = 2715 / 999
• At , how does multiplying 70.7 times 10 make the fraction correct? This is might be stupid, but I just dont get it.
• Miriam,
70.7/900 can't be a fraction because it contains a decimal, 70.7
By multiplying 70.7/99 by ten, it changes to 707/990, and since there's no decimal anymore, the fraction is acceptable.
Hope that helps!