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Without actual division show that the following rational number is a terminating decimal. Express in decimal form 171/800.

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This is the basic and exam oriented question from real numbers in which we have given a number 171/800 and we have to show that the given rational number is a terminating decimal and also asked to express in decimal form

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1C, question no 1(iii)


1 Answer

  1. Here, denominator is 800=2^5×5^2.

    Either 2 or 5 is not a factor of 171, so fraction is in its simplest form.

    Then, it can be written as:
    24/125=171/(2^5×5^2), which is similar to the form of (2^m×5^n) in denominator.

    Hence, the given rational is terminating
    and its decimal expansion is 171/800=0.21375.

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