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Question

Find the value of 0.111.... + 0.333.....

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Solution

Given operation is 0.111... + 0.333....
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...............(1)

Now we can express 0.3 as 3 × 0.111....
from (1), 0.111.... = 19
0.333...=3×19
=39
0.333.... = 13

Now, 0.111... + 0.333.... = 19+13
= 49
49=4×19
19=0.111..... [from eq(1)]
49=4×0.111... =0.444....

0.111... + 0.333.... = 0.444...

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