Fractions Worksheet Page 28
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36Fractions
3.7
Terminating and recurring
decimals
All rational numbers can be written as decimals, some of
Terminating means that the decimal
which are terminating decimals and some of which are not.
ends – there is a finite number of
decimal places.
Here are two examples of terminating decimals:
7
5 3.5
1
5 0.125
2
8
To change a fraction into a decimal you can do the
division on your calculator.
5
For example,
5 0.625
8
Only those fractions that have a denominator with prime
factors of only 2 and/or 5 can be converted to
terminating decimals.
Fractions that do not satisfy this condition convert to
decimals that repeat and do not terminate.
Look at these fractions written as decimals.
0.428571428
1
5 0.333 333 …
5
5 0.416 666 …
3
12
8
3
5 0.727 272 …
5 0.428 571 428 571 42 …
11
7
When you work out the decimal answer on your calculator,
the decimal places fill the whole of the calculator display.
This is what your calculator
display will show when you work
If you do the division by short or long division methods you
out 3 4 7.
will see that the decimals never end.
The decimals do not terminate – they are called recurring
Recurring decimals have either a
repeating digit or a repeating
decimals.
pattern of digits.
Because they never end, you need to have a way of writing
them which makes the repeating pattern clear.
When a single digit repeats, you put a dot over this digit.
5 0.333 333… is written as 0.3 ˙
1
3
5 0.416 666… is written as 0.416 ˙
5
12
Number 87
M03_CMC_SB_IGCSE_6850_U03.indd 87
9/6/09 16:45:21
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