Maths-
General
Easy

Question

Convert 17.17090090090.............. as a fraction.

Hint:

First find the decimal part as a fraction and then add it with the whole number
part.

The correct answer is: 190597/11100


    Complete step by step solution:
    Let x = 0.17090090…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 1.7090090
    Now multiply by 100 on both the sides in (i),
    100x = 17.090090
    Now multiply by 1000 on both the sides in (i),
    1000x = 170.90090
    Now multiply by 10000 on both the sides in (i),
    10000x = 1709.0090
    Now multiply by 100000 on both the sides in (i),
    100000x = 17090.090
    On subtracting 100x from both the sides, we have
    100000x - 100x = 17090.090 - 17.090090
    rightwards double arrow99900x = 17073
    rightwards double arrow x space equals space 17073 over 99900
    On simplification, we get x = 1897 over 11100
    Now we have a fraction for 0.17090090…. On adding it with 17, we have
    rightwards double arrow 17 space plus space 1897 over 11100
    rightwards double arrow 190597 over 11100 as fraction

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