1.

Write the value of 0.\(\bar{3}\).

Answer»

Let x = 0.\(\bar{3}\)

x = 0.33333 … ….

x = 0.3 + 0.03 + 0.0003 + 0.0003 + ………

∴ a = 0.3, r = \(\frac{0.03}{0.3}\) = 01 n = ∞

∴ Sum of infinite terms in G.P,S = \(\frac{a}{1-r}\)

∴ x = \(\frac{0.3}{1−0.1}\) = \(\frac{0.3}{0.9}\) = \(\frac{1}{3}\)

∴  0.\(\bar{3}\) = \(\frac{1}{3}\)


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