Question

Express 0.757575.... in the form of p/q, where p and q are integers and q is not equal to zero.

Answer 1

we can write 0.757575............ as 0.75(75 under bar)

Now,let x= 0.75(75 under bar)

x= 0.757575....... -(1)

now multiply both side by 100,

100x= 75.7575....... -(2)

now subtract equation 1 from equation 2,

100x= 75.7575......

-x= -0.7575........

__________________

99x=75

Therefore,

x=75/99

= 25/33

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