Question

How do you simplify and make the fraction 4/33 into a decimal?

Answer 1

You can long divide `4` by `33` and observe the repeating remainder, or simply notice that `4/33 = 12/99 = 0.121212... = 0.dot(1)dot(2)`

Explanation:

First note that `4` and `33` have no common factor greater than `1`, so `4/33` is already in simplest form.

When we start to long divide `4` by `33` it only takes a couple of digits to get back to the number we first started with...

So we get a repeating decimal expansion:

`4/33 = 0.121212... = 0.dot(1)dot(2)`

Alternatively, note that `4/33 = (3*4)/(3*33) = 12/99 = 0.dot(1)dot(2)`