How do you change 0.5625 into a fraction?

1 Answer
Nov 4, 2015

Since this decimal ends with #5#, see what happens when we multiply by #2#, then by #2# again, etc., eventually finding:

#0.5625 = 9/16#

Explanation:

Let's take this step by step to keep the arithmetic simple and avoid introducing unnecessary common factors...

#0.5625# ends in #5#, so multiply it by #2#:

#0.5625 xx 2 = 1.125# which ends in #5#, so multiply by #2# again:

#1.125 xx 2 = 2.25# which ends in #5#, so multiply by #2# again:

#2.25 xx 2 = 4.5# which ends in #5#, so multiply by #2# again:

#4.5 xx 2 = 9#

Having reached a whole number, notice that we have multiplied by #2# four times.

So:

#0.5625 = 9/(2^4) = 9/16#

In general, if a decimal ends with #5#, multiply it by #2#. If it ends with an even digit, multiply it by #5#. Otherwise multiply by #10#.

Repeat until you get a whole number, then that is the numerator and the denominator is the product of the multipliers you used.

For example,

#0.24 stackrel(xx 5) -> 1.2 stackrel(xx 5) -> 6#

So #0.24 = 6/(5^2) = 6/25#