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Question

Match the correct decimal form to its fractional form.

A
711
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B
79
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C
169
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Solution

Case 1:
Let 'x' be 0.636363....
In this decimal, the digits 63 gets repeated. So multilpy x with 100.

100x = 63.636363....
= 63 + 0.636363.....
= 63 + x (x=0.636363....)

99x = 63
x = 6399
= 711

Fractional form of the decimal 0.636363....... is 711.

Case 2:
Let 'x' be 0.7777777....
In this decimal, the digit 7 gets repeated. So multilpy x with 10.

10x = 7.777777....
= 7 + 0.777777.....
= 7 + x (x=0.777777....)
9x = 7
x = 79
= 79

Fractional form of the decimal 0.777777....... is 79.

Case 3:
Let 'x' be 1.7777777....

In this decimal, the digit 7 gets repeated. So multilpy x with 10.

10x = 17.777777....
= 16 + 1.777777.....
= 16 + x (x=1.777777....)
9x = 16
x = 169
= 169
Fractional form of the decimal 1.777777....... is 169.

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