year 8 maths

4C
Decimal place value and fraction/decimal conversions
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4C Decimal place value and fraction/decimal
conversions REVISION
Decimals are another way of representing ‘parts of a whole’. They are an extension of our base 10 number
system. The term decimal is derived from the Latin word decem meaning ‘ten’.
A decimal point is used to separate the whole number and the fraction part. Decimals have been studied
extensively in Year 7 . In this section we revisit the concepts of comparing decimals and converting
between decimals and fractions.
Let’s start: Order 10
The following 10 numbers all contain a whole number part and a fraction part. Some are decimals and
some are mixed numerals.
Work with a partner. Your challenge is to place the 10 numbers in ascending order.
1 5
72 1
3 2
4 3 3.3 3 3 2.85 3.09 2 3 3.9
11 6
100 3
4 5
■ When dealing with decimal numbers, the place value table is extended to involve tenths,
hundredths, thousandths etc.
■ The number 517.364 means:
Hundreds Tens Units Decimal point Tenths Hundredths Thousandths
5 1 7 . 3 6 4
5 × 100 1 × 10 7 × 1 . 3 × 1 10
3
500 10 7 .
10
6 × 1
100
6
100
4 × 1
1000
4
1000
Key ideas
■ Comparing and ordering decimals
To compare two decimal numbers with digits in the same place value columns, you must
compare the left-most digits first. Continue comparing digits as you move from left to right until
you find two digits that are different.
For example, compare 362.581 and 362.549 .
Hundreds Tens Units Decimal point Tenths Hundredths Thousandths
3 6 2 . 5 8 1
3 6 2 . 5 4 9
Both numbers have identical digits in the hundreds, tens, units and tenths columns. Only when
we get to the hundredths column is there a difference. The 8 is bigger than the 4 and therefore
362.581 > 362.549 .
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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