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what will -13.9535535535535535 be as a fraction if 535 repeats?

Guest Apr 23, 2017
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Here's how I do this

Forget the " -13" we'll add that in later

Working with the decimal, write  the non-repeating and repeating part,  9535,  and subtract the non- repeating part   =  9535 - 9  =  9526

As a denominator......write the same number of 9s as the number of digits in the repeating part of the decimal- thus, 3 "9s", followed by the same number of 0s as the number of digits in the non-repeating part of the decimal, thus, 1 "0".......thus the denominator  = 9990

So.......the decimal part of the fraction can be represented as  9526 / 9990

Add back the -13 giving the mixed number  of  - (13 + 9526/9990)

Converting this to a fraction, we have  -(139396 / 9990)

Verify this for yourself

CPhill  Apr 23, 2017
edited by CPhill  Apr 23, 2017
edited by CPhill  Apr 23, 2017

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