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

1 Answer
Mar 24, 2016

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