Maths-
General
Easy

Question

Convert the following repeating decimals to fractions
c) 0.366666666666

Hint:

Perform necessary multiplications to make it as a fraction.

The correct answer is: 11/30


    Complete step by step solution:
    (c) Let x = 0.3666666
    Now multiply by 10 on both the sides,
    We get, 10x = 3.666666
    On subtracting x 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 10 x minus x equals 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have .11 over 30 (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 11 over 30
    Hence 0.3666666…. = 11 over 30
     

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