Discussion

Explanation:

Let x = 21.376

Muliplyting both sides with 101 (There is one non recurring digit after decimal)

⇒ 10x = 213.76   ...(1)

Muliplyting both sides with 102 (There are two recurring digits after decimal)

⇒ 1000x = 21376.76   ...(2)

(2) - (1)

⇒ 1000x -10x = 21376.76 - 213.76 = 21376 - 213 = 21163

∴ x = 21163990

Alternately,
Numerator of the fraction = 21376 - 213 = 21163

Denominator = 990

∴ x = 21163990

Hence, option (a).

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