Fractions Worksheet Page 31
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36When
1
digit recurs multiply both
(a) Let
x 5 0.8888…
sides by 10.
10x 5 8.8888…
When
2
digits recur multiply both
sides by 100.
Subtracting:
9x 5 8
3
When
digits recur multiply both
sides by 1000.
8
Dividing both sides by 9:
x 5
9
(b) Let
x 5 0.454 545…
100x 5 45.454 545…
Subtracting:
99x 5 45
45
Dividing both sides by 99:
x 5
99
5
Dividing top and bottom by 9:
x 5
11
(c) Let
x 5 0.610 810 810 8…
1000x 5 610.810 810 810
Subtracting:
999x 5 610.2
You must not leave your answer as
610.2
Dividing both sides by 999:
x 5
610.2
because a fraction should
999
999
consist of whole numbers.
6102
Notice that there is still quite a lot
Multiplying top and bottom by 10: x 5
9990
of work to do to get the answer
into its simplest form.
678
Dividing top and bottom by 9:
x 5
1110
You will not score full marks if you
do not simplify fully.
113
Dividing top and bottom by 6:
x 5
185
Example 1(c) can be done another way:
This method requires two
multiplications at the start but then
Let
x 5 0.610 810 810 8…
has the advantage that the
108…
then
10x 5
6.108
recurring decimal pattern is the
same.
108…
and
10 000x 5
6108.108
When you subtract you
Subtracting:
9990x 5 6102
automatically get whole numbers
on the top and bottom of your
6102
Dividing both sides by 9990:
x 5
fraction.
9990
Both methods give you the same
113
x 5
answer.
185
You can choose whichever method you prefer, but if you
choose the second one you must remember to multiply x
by multiples of 10 which will give you the same pattern of
recurring decimals.
3
EXERCISE
P
1 Write these recurring decimals using the dot notation.
(a) 0.666 666…
(b) 0.111 111…
(c) 0.733 333…
90 Number
M03_CMC_SB_IGCSE_6850_U03.indd 90
9/6/09 16:45:22
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