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7.2 Recognising equivalent fractions, decimals and percentages

7.2 Recognising equivalent fractions, decimals and percentages

In Unit 3 you saw the connection between decimal numbers and fractions.

Hundreds Tens Units • Tenths Hundredths Thousandths Remember the decimal
place-value table.
100 10 1 s 1 1 1
10 100 1000

!e decimal number 0.1 can be written as the fraction 1 . All these decimal
10

!e decimal number 0.2 can be written as the fraction 2 , 0.3 as 3 numbers are called
terminating decimals
and so on. 10 10
because they come to
Similarly, 0.01 can be written as 1 , 0.05 as 5 , 0.15 as 15 and so on. an end.
100 100 100
To write a terminating decimal as a fraction, follow these steps.
t Write the number in the place-value table and look at the value (tenths, hundredths, ...)
of the last digit.
t Write this value as the denominator of your fraction.
t Write as the numerator the digits that come a$er the decimal point.

t Cancel the fraction to its simplest form.

Worked example 7.2A

Write the following decimal numbers as fractions in their simplest form.
a 0.7 b 0.26 c 0.045

a 0.7 = 7 The 7 is in the tenths column of the place value table. 7 cannot be cancelled.
10 10
26
b 0.26 = 100 The 6 is in the hundredths column of the place-value table.

13
26
26
100 = 50 100 can be cancelled by dividing 26 and 100 by 2.
45
c 0.045 = 1000 The 5 is in the thousandths column of the place-value table.
45 = 9 45 can be cancelled by dividing 45 and 1000 by 5.
1000 200 1000

7 Fractions 75