Step by step
The question
Question: write 5/11 as a decimal.
511
1 Divide
The bottom 11 does not go into 10, 100 or 1000.
So we divide: 5 ÷ 11, one digit at a time.
5 ÷ 11 is 0, with 5 left.
So we write 0 and the point.
5 ÷ 11 = 0, 5 left
We put a 0 next to the 5 left: 50.
50 ÷ 11 is 4, with 6 left.
50 ÷ 11 = 4, 6 left
We put a 0 next to the 6 left: 60.
60 ÷ 11 is 5, with 5 left.
5 left again: the same as before.
So the digits repeat for ever.
60 ÷ 11 = 5, 5 left
So 5/11 is 0.4545…, and the 45 repeats for ever.
= 0.4545…
the 45 repeats
A repeating decimal never ends.
So we cannot multiply it back exactly.
The same leftover coming back is our check.
Answer
the 45 repeats