CBSE Class 10-Mathematics: Chapter –1 Real Numbers Part 12
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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.