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January 30, 2015

January 30, 2015

Posted by **Greg** on Tuesday, December 11, 2007 at 9:55pm.

- pre-Algebra -
**Reiny**, Tuesday, December 11, 2007 at 10:12pmHere is a neat algorithm to change any repeating decimal into an exact fraction

Assume you have only the decimal portion of your number, ie, for 4.5676767... consider only the 5676767..

For the numerator, write down all the digits to the end of your repeat, subtract from that the part that does not repeat.

For the denominator, write down a 9 for each digit in the repeating loop, followed by the number of digits that don't repeat.

e.g. 0.45676767..

=(4567-45)/9900

=4522/9900, now reduce to

2261/9900

your number would be

.833333. = (83-8)/90

= 75/90

= 5/6

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