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Express Each of the Following as a Rational Number in Its Simplest Form: (I) `0. Bar (12)` - Mathematics

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Express each of the following as a rational number in its simplest form:

(i) `0. bar (12)`

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Solution

Let x =`  0. bar (12)`
∴ x = 0.1212               …(1)
100x = 12.1212                          …(2)
On subtracting equation (1) from (2), we get
99x = 12 ⇒ x = `4/33`
∴0.12 = `bar (4)/33`

Concept: Euclid’s Division Lemma
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