Fractions and decimals
The question
as a decimal
0.3 31.0 91
- The line in a fraction has always been a division sign: means 1 ÷ 3.
- 3 does not go into 1, so write a point and put zeros after it. 1 is the same amount as 1.0 — the zeros change nothing, they just give the division room to keep going.
- 10 ÷ 3 = 3, leaving 1.
- The remainder has come around to one we have had before, so from here the digits just repeat. = 0.3 repeating.
How it works.
- 01
The line in a fraction has always been a division sign: 1/3 means 1 ÷ 3.
- 02
3 does not go into 1, so write a point and put zeros after it. 1 is the same amount as 1.0 — the zeros change nothing, they just give the division room to keep going.
- 03
10 ÷ 3 = 3, leaving 1.
- 04
The remainder has come around to one we have had before, so from here the digits just repeat. 1/3 = 0.3 repeating.