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| Changing a Recurring Decimal to a Fraction |
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Examples
This is a common question and requires good preparation.
Example 1: Change 1,7777… to a fraction.
Method:
| Let x = 1,7 |
then |
10x |
= |
17,7 |
and subtracting gives |
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9x |
= |
16 |
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x |
= |
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x |
= |
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Example 2: Change 0,3232323232… to a fraction.
Let x = 0,32323232…(Because there are two figures recurring, multiply by 100).
100x = |
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32,323232… |
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x = |
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0,323232… |
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(subtracting) |
99x = |
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32 |
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x = |
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 |
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Example 3: Change 0,084848484… to a fraction.
(Note: The 0 is not recurring).
1 000x |
= |
84 |
,848484… |
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(x 1 000 to move the point) |
10x |
= |
0 |
,848484… |
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(x 10 to move the point) |
990x |
= |
84 |
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(subtracting) |
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= |
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(cancel) |
x |
= |
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