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1. Subtitle

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How do we convert repeating,
non-terminating decimals?
Study the following examples.

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Example 1. Change 0. 𝟒 to fraction.
Step 1: Let n = 0. 𝟒
Step 2: Multiply both sides of the
equation in step 1 by 10.
We use 10 as the multiplier because
there is only one repeating digit. If
there are two repeating digits, we
shall use 100 as multiplier.
(n = 0. 𝟒) 10
10n = 4. 𝟒
Step 3: Subtract the equation in
step 1 from the equation in Step 2.
10n = 4. 𝟒
- n = 0. 𝟒
9n= 4
Divide both sides of the equation by
the coefficient of n.
𝟗𝒏
𝟗
=
𝟒
𝟗
n =
𝟒
𝟗

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Example 2. Change 0.𝟐𝟕 to fraction.
Step 1: Let n = 0.27
Step 2: Multiply the equation in
step 1 by 100.
(n = 0.27)100
100n = 27 .27
Step 3: Subtract the equation in
step 1 from the equation in step 2.
100n = 27.27
- n = 0. 27
99n = 27
99𝑛
99
=
27
99
n =
27
99
(9)
n =
𝟑
𝟏𝟏