Question

How do you convert 0.312 (12 repeating) to a fraction?

Answer 1

`a=103/330`

Explanation:

Let the desired number be `a=0.3bar (1 2)` .......(1)

Multiply both sides with `100` to obtain, as there are 2 repeated digits so multiply with `10^2`
`100xxa=100xx0.3bar (1 2)`
`100a=31.2bar (1 2)` ......(2)
Subtracting (1)from (2)

`100a-a=31.2bar (12)-0.3bar(12)`, simplify and solve for `a`
`99a=30.9`
`a=30.9/99`, get rid of decimal and simply
`a=cancel 309^103/ cancel 990^330`
`a=103/330`