How to express 0.2545454... as a fraction in it's simplest form?
2 Answers
Explanation:
Explanation:
A common notation to indicate the repeating part of a decimal representation is a viniculum - a bar placed above the group of digits that repeat.
So we can write
To find an equivalent fraction, first multiply by an integer that will give an integer product.
A suitable multiplier is
#10(100-1)0.2bar(54) = (100-1)2.bar(54) = 254.bar(54) - 2.bar(54) = 252#
Then divide both ends by
#0.2bar(54) = 252/(10(100-1)) = 252/990 = (14 * color(red)(cancel(color(black)(18))))/(55 * color(red)(cancel(color(black)(18)))) = 14/55#