Question

How do you convert -0.01 (01 being repeated) to a fraction?

Answer 1

`1/90`

Explanation:

Require to obtain 2 equations with the same repeating part after the decimal point and subtract them to eliminate the repeating part.

Begin with letting x = 0.0111111111...............

To obtain the repeating part after the decimal point need to multiply by 10.

hence 10x = 0.111111111111111....................... (A)

Require a second equation with repeating part after decimal point.
Multiply by 100.

100x = 1.1111111111111111.............................. (B)

Subtracting (A) from (B) will eliminate repeating part.

thus (B) - (A) gives 90x = 1 `rArr x = 1/90`