How do you convert 4.078 (78 being repeated) to a fraction?

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Answer 1 · 2016-03-02T10:47:19

$2019/445$

Let $4.0787878787878...........=x$

Multiplying this by $10$ , we get

$10x=40.787878787878...........$ -----------------(A)

Multiplying (A) by $100$ , we get

$1000x=4078.787878787878...........$ -----------------(B)

Now subtracting (A) from (B), we get

$990x=4038$ i.e.

$x=4038/990=2019/445$