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Express Each of the Following as a Rational Number in Its Simplest Form: (I) `0. Bar (24)` - Mathematics

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

(i) `0. bar (24)`

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Solution

Let x = ` 0. bar (24)`
∴ x = 0.2424                …(1)
100x = 24.2424                        …(2)

On subtracting equation (1) from (2), we get
99x = 24 ⇒ x = `8/33`
∴0.24 = `bar(8)/33`

Concept: Euclid’s Division Lemma
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