Question 54

When 0.090909.....is converted into a fraction, then the result is

Solution

Let $$x$$ = 0.090909.... --------------(i)

Multiplying both sides by 100

=> $$100x$$ = 9.090909.... ------------(ii)

Subtracting equation (i) from (ii)

=> $$100x - x$$ = (9.090909....) - (0.090909....)

=> $$99x = 9$$

=> $$x = \frac{9}{99} = \frac{1}{11}$$

So, 0.090909....written in the form p/q is 1/11

=> Ans - (B)

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