How do you convert 1/3 into a decimal and percent?

1 Answer
May 21, 2016

#1/3# as a decimal #->0.3bar3#

#1/3# as a percentage #->(33.3bar(3))/100 -> 33.3bar(3)%#

Explanation:

#color(blue)("Determining the decimal value of "1/3)#

If you apply long division you soon observe a repeating pattern. You would have demonstrated that this pattern goes on forever. The number is:

#0.3333333333333.....#

The mathematical way to show the repeating process is to put a bar over the last 3 that you write. So you would get:

#0.3bar3#
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determining the percentage equivalent of "1/3)#

The first decimal place is #1/10color(white)()^("ths")#

The second decimal place is #1/100color(white)()^("ths")#

As percentage is really #1/100color(white)()^("ths")# then we would write:

#(33.3bar(3))/100 -> 33.3bar(3)%#