Maths-
General
Easy

Question

Express the following recurring decimals as vulgar fraction
b) 0.743434343......

Hint:

Perform necessary multiplications to make it as a fraction.

The correct answer is: 368/495


    Complete step by step solution:
    (b)  Let x = 0.743434343…(i)
    Now multiply by 10 on both the sides in (i),
    We get, 10x = 7.434343
    Now multiply by 100 on both the sides in (i),
    100x = 74.3434343
    Now multiply by 1000 on both the sides in (i),
    1000x = 743.434343
    On subtracting 10x from both the sides, we have
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1000 x minus 10 x equals 743.434343 minus 7.43434343 end cell row cell not stretchy rightwards double arrow 990 x equals 736 end cell row cell not stretchy rightwards double arrow x equals 736 over 990 end cell end table
    On simplification, we have x equals 368 over 495
    Hence 0.7434343434....... = 368 over 495

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