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.