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Question

Find the value of (0.333....)2 in decimal form.

A
0.666.....
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B
0.999.....
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C
0.111.......
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D
0.333......
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Solution

The correct option is C 0.111.......
Given operation is (0.333....)2
Now, 0.333....=3×0.111...............(1)
Let 'x' be 0.111....
Multilpy x with 10.
10x = 1.11....
= 1 + 0.111....
= 1 + x (x=0.111....)
9x = 1
x = 19
0.111.... = 19................(2)

Substituting the value of 0.111... in (1) we get,
0.333....=3×19
=13

(0.333....)2=(13)2
=19
19=0.111.... [from eq (2)]
(0.333....)2=0.111.....

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