How do you convert 2.7812 (12 repeating) to a fraction?

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How do you convert 2.7812 (12 repeating) to a fraction?

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Answer 1 · 2016-03-09T20:59:09

The answer is $4589/1650$

Explanation:

Consider $x=2.781212...$
$10^2x=278.1212...$
$10^4x=27812.1212...$
the difference will give us :
$10^4x-10^2x=27812.1212...-278.1212...=27534$
so : $9900x=27534$
therefore : $x=27534/9900=4589/1650$

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How do you convert 2.7812 (12 repeating) to a fraction?

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