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Explain 0.23(bar on 23) as a rational number in simplest form

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This question is taken from real numbers chapter in which we have given a number 0.23(bar on 23) and we have to show that the given number is a rational number in its simplest form.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1E, question no 19


1 Answer

  1. Let x=0.23(bar on 23)…(i)

    multiply 100 on both sides-
    100x=23.23 (bar on 23)….(ii)

    Subtract the equation (i) from (ii)
    So, x=23/99

    Simplest form of 0.23(bar on 23) as rational number is 23​/99.

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