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Maths-

General

Easy

Question

Without doing any actual division, find which of the following is a terminating decimal or not: $123 over 125$

hint Hint:

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: terminating decimal

Let x = p/q be a rational number such that the prime factorisation of q is in form 2^m5ⁿ, where m and n are non-negative integers, then x will have a terminating decimal expansion.
$x equals 123 over 125$
In the given rational number, the value of q is 125. The factorisation of 125 is given as
$125 equals 5 cubed equals 2 to the power of m 5 to the power of n$
Final Answer:
As the factorisation of 125 is in the form of 2^m5ⁿ, $23 over 175$ will have terminating decimal expansion.

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