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Question

Find the value of 0.444.... in decimal form.

A
0.222.....
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B
0.444.....
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C
0.666....
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D
0.888....
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Solution

The correct option is C 0.666....
Given operation is 0.444....
Now, 0.444....=4×0.111...............(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,
0.444....=4×19
=49
0.444....=49
=23
=(23)×(33)
=69
19=0.111.... [from eq (2)]
0.444....=6×0.111.....
=0.666......

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