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Question

Convert given Non-terminating repeating decimal into fraction
0.069696969........

A
6999
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B
23330
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C
23990
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D
None of the above
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Solution

The correct option is B 23330
Let 0.0696969...... = K ...........(1)
Multiplying both side by 100 we get,
6.96969........=100K .........(2)
Substracting equation (1) from equation (2) we get
6.96969....0.06969....=100KK
6.9=99K
K=6.999
Removing decimal we get,
K=69990
On simplifying we get,
K=23330.

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