Maths-
General
Easy

Question

Without performing the actual division, check whether the following rational numbers are terminating or non-terminating.23 over 175

hintHint:

Hint:
Numbers with a fixed or finite number of digits following the decimal point are known as terminating decimals and numbers with infinite decimal places are known as non-terminating decimals.

The correct answer is: non-terminating decimal expansion.


    Let x = p/q be a rational number such that the prime factorisation of q is in form 2m5n, where m and n are non-negative integers, then x will have a terminating decimal expansion.
    a)
    x = bevelled 23 over 175
    In the given rational number, the value of q is 175. The factorisation of 175 is given as
    175 equals 5 squared cross times 7 not equal to 2 to the power of m 5 to the power of n
    Final Answer:
    As the factorisation of 175 is not in the form of 2m5n, bevelled 23 over 175 will have non-terminating decimal expansion.

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