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Explain 0.4(bar on 4) as a rational number in simplest form

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This question is taken from real numbers in which we have given a number 0.4(bar on 4) and we have to show that the given number is a rational number in its simplest form.

Kindly solve the above problem in details

RS Aggarwal, Class 10, chapter 1E, question no 10


1 Answer

  1. Let x=0.4(bar on 4)…(i)

    multiply by 10 on both sides-
    10x=4.4(bar on 4)….(ii)

    Subtract the equation (i) from (ii)
    So, x=4/9

    Simplest form of 0.4(bar on 4) as a rational number is 4/9.

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