Q. 8 A5.0( 2 Votes )

# Find the rational numbers having the following decimal expansions :

Answer :

Let,

x = 0.33333333…..

x = 0.3 + 0.03 + 0.003 + …∞

⇒ x = 3(0.1 + 0.01 + 0.001 + …∞ )

⇒ x =

We observe that the above progression possess a common ratio. So it is a geometric progression.

Common ratio = 1/10 and first term (a) = 1/10

Sum of infinite GP = ,where a is the first term and k is the common ratio.

Note: We can only use the above formula if |k|<1

∴ we can use the formula for the sum of infinite GP.

⇒ x = 3×

∴ x = 1/3

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