Maths-

General

Easy

Question

# Without performing the actual division, check whether the following rational numbers are terminating or non-terminating

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: non-terminating decimal expansion.

### Let x = p/q be a rational number such that the prime factorisation of q is in form 2^{m}5^{n}, where m and n are non-negative integers, then x will have a terminating decimal expansion.

x =

The given rational number is not in its simplified form. So, let’s first covert it in the simplified form

x =

In the simplified rational number, the value of q is 13. The factorisation of 13 is given as

Final Answer:

As the factoriation of 13 is not in the form of 2^{m}5^{n}, will have non-terminating decimal expansion.

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