Question

Question #0426c

Answer 1

`0.8bar(7) = 79/90`

Explanation:

Let `x = 0.8bar(7)`

`=> 10x = 8.bar(7)`

`=> 10x - x = 8.bar(7) - 0.8bar(7)`

`=> 9x = 8.7 - 0.8`

`=> 9x = 7.9`

`=> 9x = 79/10`

`=> x = 79/10*1/9`

`:. x = 79/90`

This technique of multiplying by `10` (or a power of `10`) and subtracting can be used to find the fractional representation of any number with infinitely repeating decimal digits. This answer contains a detailed explanation.