Question 22793: I am trying to explain an answer to my son but I am having a hard time rememberng this from high school. The problem is:
.13 where the 3 goes on for infinity
He is to put the number in a fraction form
I thought it would be just 13/100 but I recall in his book last night (he didn't bring the book home tonight) that you multiply by 100 then subtract one so the answer would be something like 13/99?
Help....
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Here's how you do these: To convert repeating decimals to an equivalent fraction, isolate the repeating group as an integer, in this case, the repeating group is .13, using the following technique:
Let:
n = 0.131313...Now multiply n by 100 to isolate the repeating group of .13
100n = 13.131313... Subtract n from 100n = 99n.
99n = 13.131313 -0.131313 = 13
So, 99n = 13 Divide both sides by 99
n = 13/99 but n is 0.131313...
So, 0.131313... = 13/99 Check this out on your calculator.
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