Write 1/3 as a decimal

Step by step

The question

Question: write 1/3 as a decimal.

1 Divide

The bottom 3 does not go into 10, 100 or 1000.

So we divide: 1 ÷ 3, one digit at a time.

1 ÷ 3 is 0, with 1 left.

So we write 0 and the point.

We put a 0 next to the 1 left: 10.

10 ÷ 3 is 3, with 1 left.

1 left again: the same as before.

So the digits repeat for ever.

So 1/3 is 0.333…, and the 3 repeats for ever.

A repeating decimal never ends.

So we cannot multiply it back exactly.

The same leftover coming back is our check.