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Question

Find the decimal form of 19.

A
0.1111......
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B
0.99999.....
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C
0.191919....
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D
0.333333
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Solution

The correct option is A 0.1111......
Given fraction is 19.
19 = 19 × 1010
= (109) × 110
= (119) × 110
= (1+19) × 110
= 110 + 190.......(1)

Now, 190 = 19×10
= (19) × 110.......(2)
From (1), 19 = 110 + 190; substitute it in eq (2).

190 = (110 + 190) × 110

= 1100 + 1900
Now substituting this value in eq(1), we get

19 = 110 + (1100 + 1900)

= (110 + 1100) + 1900

Similarly finding the value of 1900=(19×1100)
and on solving that will give 11000 + 19000

19 = 110 + 1100 + (11000 + 19000)

This cycle will continue and leads to 11 = 110 + 1100 + 11000 + 110000 + ........
= 0.1 + 0.01 + 0.001 + 0.0001 + .....

19 = 0.1111.....

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