CBSE Class 10-Mathematics: Chapter – 1 Real Numbers Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 2:

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion.

Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Answer:

According to Theorem, any given rational number of the form where and are co-prime, has a terminating decimal expansion if q is of the form , where and are non-negative integers.

(i)

Here, denominator is of the form , where and .

It means rational number has a terminating decimal expansion.

(ii)

Here, denominator is of the form , where and .

It means rational number has a terminating decimal expansion.

(iii)

Here, denominator is not of the form , where and are non-negative integers.

It means rational number has a terminating decimal expansion.

(v)

Here, denominator is not of the form , where m and n are non-negative integers.

It means rational number has non-terminating repeating decimal expansion.

(vi)

Here, denominator is of the form , where and are non-negative integers.

It means rational number has terminating decimal expansion.

(vii)

Here, denominator is not of the form , where and are non-negative integers.

It means rational number has non-terminating repeating decimal expansion.

(viii)

Here, denominator is of the form , where and .

It means rational number has terminating decimal expansion.

(ix)

Here, denominator is of the form , where and .

It means rational number has terminating decimal expansion.

(x)

Here, denominator is not of the form , where and are non-negative integers.

It means rational number has non-terminating repeating decimal expansion.