How do you change 0.5625 into a fraction?

Question

Julia Adams · Accepted Answer

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#

Let's go over this step-by-step to keep the math straightforward and steer clear of adding needless 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. Thus: #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#. Continue until you obtain a whole number; this is the numerator, and the multiplier product you used is the denominator. As an illustration, #0.24 stackrel(xx 5) -> 1.2 stackrel(xx 5) -> 6# So #0.24 = 6/(5^2) = 6/25#

Genesis Allen · Answer

undefined To change 0.5625 into a fraction, you can express it as $ \frac{5625}{10000} $. Then, you can simplify the fraction to its lowest terms if needed.