Express 1.272727... in the form of p/q

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Solution

Let x = 1.272727....------( 1 )

Multiply ( 1 ) with 100 we get

100x = 127. 272727... ----( 2 )

Subtract ( 1 ) from ( 2 ) we get

99x = 126

x = 126/ 99

x = ( 9 × 1 4)/ ( 9 × 11 )

After cancellation

x = 14/11 ( p / q form )

Therefore

1.272727...= x = 14/11

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