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

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

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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