What is 0.036 where the 6 is recurring as a fraction?

Answer 1

36/900 = 12/300 = 1/25 = 0.4

Let's break 0.036r (I am using the 'r' to mean recurring) into two parts

0.036r = 0.03 + 0.006r

0.03 = 3/100

0.006r = 6/900

So 0.036r = 3/100 + 6/900 = 27/900 + 6/900 = 33/900 = 11/300

Answer 2

I got 11/300 too, but I got to it this way:
I recognized the number as 3 2/3 divided by 100, so I converted 3 2/3 to 11/3 then multiplied by 1/100.

Answer 3

You have :

3.666666........ = 3 2/3 = 11/3

0.366666......... = 11/30

0.0366666....... = 11/300 <-----------------------