How do you convert 2.136 (36 repeating) as a fraction?
1 Answer
Explanation:
There is a notation for repeating decimals that places a bar above the repeating pattern.
Using that notation, the original decimal representation is written:
#2.1bar(36)#
To make this into an integer, multiply by
#(1000-10)*2.1bar(36) = 2136.bar(36) - 21.bar(36) = 2115#
Then divide both sides by
#2.1bar(36) = 2115/(1000-10) = 2115/990 = (color(red)(cancel(color(black)(3*3*5)))*47)/(color(red)(cancel(color(black)(3*3*5)))*22) = 47/22#