year 8 maths

224 Chapter 4 Fractions, decimals, percentages and financial mathematics
Key ideas
■ Rounding decimals involves approximating a decimal number to fewer decimal places. When
rounding, the critical digit is the digit immediately after the rounding digit.
• If the critical digit is less than 5, the rounding digit is not changed.
• If the critical digit is 5 or more, the rounding digit is increased by 1.
For example: 51.34721 rounded to two decimal places is 51.35 .
The critical digit is 7 , which is greater than 5 , hence the rounding digit is increased by 1 .
An illustration of rounding to one decimal place:
The decimals 7.41 to 7.44 are closer in value to 7.4 and will all round to 7.4 .
The values 7.46 to 7.5 are closer in value to 7.5 and will all round to 7.5 .
7.45 also rounds to 7.5 .
7.4
7.41
7.42
7.43
7.44
7.45
7.46
7.47 7.48 7.49 7.5
These values are
closer to 7.4 and
round to 7.4.
These values are
closer to 7.5 and
round to 7.5.
Example 14 Writing terminating decimals
Convert the following fractions to decimals.
1
a
4
b
7
8
SOLUTION
EXPLANATION
1
a
4 = 0.25 0. 2 5
4⟌1. 1 0 2 0
7
b
8 = 0.875 0. 8 7 5
8⟌7. 7 0 6 0 4 0
Example 15 Writing recurring decimals
Express the following fractions as recurring decimals.
2
a
b 3 5 3
7
SOLUTION
EXPLANATION
2
a
3 = 0.6. 0. 6 6…
3⟌2. 2 0 2 0 2 0
b 3 5 7 = 3.7. 14285 . 0. 7 1 4 2 8 5 7…
or 3.714285
7⟌5. 5 0 1 0 3 0 2 0 6 0 4 0 5 0 1 0
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.