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#