Express the given repeating decimals as a fraction.(1) 0.929292...(2) 52.31272727...

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- Aug 13th 2010, 05:21 AMfdrhs1984Repeating Decimals As Fraction
Express the given repeating decimals as a fraction.(1) 0.929292...(2) 52.31272727...

- Aug 13th 2010, 06:28 AMSudharaka
- Aug 13th 2010, 06:29 AMmr fantastic
Here is the slacker's way:

S = 0.929292..... eqn (1)

100S = 92.9292.... eqn (2)

Eqn (2) - eqn (1): 99S = 92 => S = 92/99.

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S = 52.31272727.... eqn (1)

100S = 5231.272727.... eqn (2)

10000S = 523127.2727..... eqn (3)

Eqn (3) - eqn (2): etc. - Aug 13th 2010, 06:43 AMearboth
1. Let n denote the number of the repeated decimals. Then you can use the following 2 equations:

The exponent of the base 10 corresponds to n.

3. Now subtract the first equation from the second cloumnwise and you'll get:

Solve for x and simplify if possible:

4. With your 2nd example you have to multiply first to get an immediately repeating decimal before you can use the described method:

Subtract the last two equations:

I'll leave the rest for you.

EDIT: ... too late - again. - Aug 13th 2010, 07:32 AMfdrhs1984
- Aug 13th 2010, 07:39 AMundefined
Simpler maybe, but I don't think it's fair to call it better. I think they're equally good.

More info on the Wikipedia page on geometric series. - Aug 13th 2010, 10:58 AMfdrhs1984