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Without actual division show that the following rational number is a terminating decimal. Express in decimal form 19/3125

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We have given a number 19/3125 and we have to prove that the given rational number is a terminating decimal and also asked to express in decimal form without actual division.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, Chapter 1C, question no 1(vi)


1 Answer

  1. Here, denominator is 3125=2^5.

    The rational number can be written as:
    19/3125=19/(2^0×5^5), which is similar to the form of (2^m×5^n) in denominator.

    Hence, the given rational is terminating,
    and its decimal expansion is 19/3125=0.00608.

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