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August 27, 2014

August 27, 2014

Posted by **HLD** on Tuesday, October 9, 2012 at 11:00pm.

Thanks. :)

- Algebra -
**Reiny**, Tuesday, October 9, 2012 at 11:16pmI will illustrate with an example

4.5676767...

let's just work on the decimal .5676767...

let x = .5676767...

multiply by 100 , (because 2 digits repeat, so 2 zeros in 100)

100x = 56.7676767

subtract ...

99x = 56.2

x = 56.2/99 = 562/990 = 281/495

so 4.5676767.. = 4 281/495 or 2261/495

quick way:

for the numerator,

--->write down all the digits to the end of the first repeat ---- 567, subtract the non-repeating digits

567-5 = 562

for the denominator, for one complete period, we have 1 leading non-repeating followed by 2 repeating ,so

put down a 9 for each repeating digit (so 2 9's) followed by a 0 for each non-repeating digit, (so one 0)

or 990

.567676767... = 562/990 = 281/495

e.g. .34123123123...

- (34123 - 34)/99900 = 34089/99900

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