year 8 maths

266 Chapter 4 Fractions, decimals, percentages and financial mathematics
Decimals as fractions
7 1 2
3.712 = 3 + + +
10 100 1000
3712 464
3.712 = =
1000 125
28 7
0.28 = =
100 25
Fractions to decimals
× 25
1 25
= = 0.25
4 100
× 25
0.3 7 5
3
= 0.375
8
8 3. 0 0 0
2
= 0.2222...
9
= 0.2
0.2 2 2...
9 2.0 0 0...
Addition and subtraction
Keep decimals places
in line.
Multiplying or dividing
by powers of 10
3.672 × 100 = 367.2
47.81 ÷ 100 = 0.4781
9.807
+ 26.350
11
36.157
−
20 15 9
216.04
38.57
177.47
Terminating decimals
0.24, 0.0381, 2.6
Recurring decimals
0.55555... = 0.5
0.4713 713 713... = 0.4 713
= 0.4 713
Decimals
Multiplication
• Multiply without decimals.
• Count decimal places in question.
• Answer has this many decimal places.
Rounding decimals
When the critical digit is 5 or more,
increase the rounding digit by 1.
Division
Multiply by powers of ten to make
divisor an integer.
681
× 52
1362
+ 34 050
35 412
681 × 5.2 = 3541.2
68.1 × 5.2 = 354.12
6.81 × 5.2 = 35.412
6.81 × 0.52 = 3.5412
0.681 × 0.52 = 0.35412
0.0681 × 0.52 = 0.035412
Rounding to two
decimal places
2.34 6
2.34 2
2.34 5
5.89 9
5.99 9
2.35
2.34
2.35
5.90
6.00
−3.826 × 100
−0.02 × 100
−382.6
−2
= 191.3
or
−3.826 ÷ −0.02
= −382.6 ÷ −2
1 9 1 . 3
= 2 3 8 2 . 6
= 191.3
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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