# Express Each of the Following as a Rational Number in Its Simplest Form: (I) 2. Bar (24) - Mathematics

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

(i) 2. bar (24)

#### Solution

Let x =  bar (2.24)
∴ x = 2.2444                    …(1)
10x = 22.444                    …(2)
100x = 224.444                  …(3)
On subtracting equation (2) from (3), we get
90x = 202 ⇒ x = 202/90 = 101/45
∴ bar (2.24) = 101/45

Concept: Euclid’s Division Lemma
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