How do you convert 0.39 (39 repeating) to a fraction?

1 Answer
Feb 22, 2016

We first assign this value as x

#x = .399999999 . . .#

Then we can multiply the value so that the decimal moves to the right a couple of spaces

#100x = 39.999999999 . . .#
and
#10x = 3.9999999999 . . . #

Let's see, how can we get rid of all of those 9's now?

Ah! Subtraction!!

We can subtract the #10x# from the #100x#!

#100x = 39.9999999999 . . . #
#10x = 3.9999999999 . . . #

#90x = 36#

#x = 36/90#

#x = 2/5#

Wow that was so easy!

Just remember: Multiply a repeating decimal by a multiple of ten so that the repeating part of the decimal can cancel out when we subtract the two numbers.