How do you convert fractions to decimal representations e.g. #7/8# and #13/20# ?

1 Answer
George C.
Dec 8, 2017

Use long division.

Explanation:

One method that always works is long division.

Keep going until the remainder is #0# or it repeats. If it is #0# then the decimal representation terminates. If not, then the decimal representation repeats as the remainder repeats.

For the two examples you give, we find:

#color(white)(00")")underline(color(white)(0)0color(black)(.)8color(white)(0)7color(white)(0)5)#
#8color(white)(0)")"color(white)(0)7color(black)(.)0color(white)(0)0color(white)(0)0#
#color(white)(00")"0)underline(6color(white)(.)4)#
#color(white)(00")"00)color(white)(.)6color(white)(0)0#
#color(white)(00")"000)underline(5color(white)(.)6)#
#color(white)(00")"00)color(white)(.)color(white)(00)4color(white)(0)0#
#color(white)(00")"00)color(white)(.)color(white)(00)underline(4color(white)(0)0)#
#color(white)(00")"00)color(white)(.)color(white)(0000)0#

So: #7/8 = 0.875#

#color(white)(0000")")underline(color(white)(000)0color(black)(.)6color(white)(0)5)#
#2color(white)(0)0color(white)(0)")"color(white)(0)1color(white)(0)3color(black)(.)0color(white)(0)0#
#color(white)(0000")")color(white)(0)underline(1color(white)(0)2color(white)(.)0)#
#color(white)(0000")")color(white)(000)1color(white)(.)0color(white)(0)0#
#color(white)(0000")")color(white)(000)underline(1color(white)(.)0color(white)(0)0)#
#color(white)(0000")")color(white)(0000000)0#

So: #13/20 = 0.65#

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