year 8 maths

212 Chapter 4 Fractions, decimals, percentages and financial mathematics
Key ideas
■ Converting decimals to fractions (non-calculator)
• Count the number of decimal places used.
• This is the number of zeros that you must place in the denominator.
• Simplify the fraction if required.
For example: 0.64 = 64
100 = 16
25
■ Converting fractions to decimals (non-calculator)
• If the denominator is a power of 10 , simply change the fraction directly to a decimal from
your knowledge of its place value.
239
For example:
1000 = 0.239
• If the denominator is not a power of 10 , try to find an equivalent fraction for which the
denominator is a power of 10 and then convert to a decimal.
3
For example:
20 = 3 × 5
20 × 5 = 15
100 = 0.15
• A method that will always work for converting fractions to decimals is to divide the
numerator by the denominator. This can result in terminating and recurring decimals and is
covered in Section 4E.
A fraction is equivalent to a division operation. In spreadsheets
and some calculators fractions and division operations are
typed the same way, using a solidus or slash (/) between the
numbers.
Example 7
Comparing decimals
Compare the following decimals and place the correct inequality sign between them.
57.89342 and 57.89631
SOLUTION
EXPLANATION
57.89342 < 57.89631 Digits are the same in the tens, units, tenths and
hundredths columns.
Digits are first different in the thousandths
column.
3
1000 < 6
1000
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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