Question

Eupress he follosing recurring decimals as the ratiornal number p/q where P and q are integers and q not equal to Zero.

0.13

0.67​

Answer 1

Your Answer is given below

1) 0.13

let,

x=0.13

Which can be written as x=0.1313 since we note that 13 is repeating.So we multiply both sides with 100.

x=0.1313 ------>e.q 1

100 (x=0.1313)

100x = 13.13

100x = 13.13------>e.q 2

By subtracting e.q 1 and e.q 2

100x - x = 13.13 - 13

99x = 13

x = 13\99

2) 0.67

let,

x=0.67

Which can be written as x=0.6767 since we note that 67 is repeating.So we multiply both sides with 100.

x=0.6767 ------>e.q 1

100 (x=0.6767)

100x = 67.67

100x = 67.67------>e.q 2

By subtracting e.q 1 and e.q 2

100x - x = 67.67 - 67

99x = 67

x = 67\99

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