Foundation
Mathematics Foundation
Properties of Real Number
Recurring Decimal Number
Rational Numbers
Question
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
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Solution
We have,
So, the denominator 8 of the given rational number is of the form , where m,n are non-negative integers.
Hence has terminating decimal expansion. the decimal expansion of terminates after places of decimals.