Write 2/3 as a decimal

Step by step

The question

Question: write 2/3 as a decimal.

1 Divide

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

So we divide: 2 ÷ 3, one digit at a time.

2 ÷ 3 is 0, with 2 left.

So we write 0 and the point.

We put a 0 next to the 2 left: 20.

20 ÷ 3 is 6, with 2 left.

2 left again: the same as before.

So the digits repeat for ever.

So 2/3 is 0.666…, and the 6 repeats for ever.

A repeating decimal never ends.

So we cannot multiply it back exactly.

The same leftover coming back is our check.