How do you convert 3.142 (142 repeating) as a fraction?

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Answer 1 · 2016-03-10T22:38:25

$3.bar(142) = 3139/999$

Multiply by $1000-1$ to shift the number three places to the left and subtract the original to eliminate the repeating decimal tail...

$(1000-1)*3.bar(142) = 3142.bar(142) - 3.bar(142) = 3139$

Dividing both sides by $(1000-1)$ we find:

$3.bar(142) = 3139 / (1000-1) = 3139/999$

This improper fraction is in lowest terms, since:

$3139 = 43 * 73$

$999 = 3*3*3*37$

So $3139$ and $999$ have no common factors larger than $1$ .