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#