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Express Each of the Following as a Rational Number in Its Simplest Form: (I) `2. Bar(4)` - Mathematics

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Express each of the following as a rational number in its simplest form:
(i) `2. bar(4)`

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Solution

Let x = `2.bar(4)`
∴ x = 2.444                  …(1)
10x = 24.444                     …(2)
On subtracting equation (1) from (2), we get
9x = 22 ⇒ x = `22/9`
∴2.4 = `bar(22)/9`

Concept: Euclid’s Division Lemma
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