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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