Download N10 - Fractions and decimals

GCSE Mathematics (1-9) 2015
How To Do it
N10Theory
Number - Decimals and fractions - Skill 10
work interchangeably with terminating decimals and their corresponding fractions
; change recurring decimals into their corresponding fractions and vice versa
1
Change fraction to a decimal
The easiest way is with a calculator so for 3/8 it is 3 ÷ 8 = 0.375
On paper we have to use division:
. 3 7 5
8 3 . 0 0 0
2
4
6 0
5 6
4 0
4 0
0
2
Change decimal to a fraction
A decimal is a fraction out of 10, or a 100, and so on. So for example
0.375 = 375/1000
0.81 = 81/100
0.02 = 2/100
0.102 = 102/100
2.58 = 258/100
Usually these will not be in lowest form, so need cancelling down:
0.375 = 375/1000 = 15/40 (cancelling by 25)
= 3/8 ( cancel by 5)
3
Fractions to recurring decimals
When some fractions are written as decimals, they do not end:
1/11 = 0.0909090909...
GCSE Mathematics (1-9) 2015
How To Do it
N10Theory
More examples
Fraction Decimal
1/3
0.3333333..
1/6
0.166666666..
1/7
0.142857142857142857142857...
1/9
0.1111111111111...
4/9
0.4444444444444444..
22/7
3.142857142857142857..
9/11
.8181818181818181..
Note these recurring decimals are different from irrational numbers like π or √2 - their
decimal versions do not repeat.
4
Recurring decimal to fraction
We use some algebra. Get two equations with the repeating parts the same,
and subtract.
For example, 0.0131313
x = 0.0131313
So we need 2 equations that go .131313..
1000x = 13.131313..
10x = .13131313..
subtract
990x=13
x = 13/990
Another example: 0.312312312
x = .312312312
1000x = 312.312312312
subtract
999x=312
x = 312/999 = 104/333