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Question:
- Since this number has a terminating decimal expansion of the form
and q is of the form
. Hence, prime factors of q will either be 2 or 5 or both.
The decimal expansion is neither terminating nor recurring. Hence, the given number is an irrational number.
Since the decimal expansion is non-terminating yet recurring.Hence the given number is of the form
and q will not be of the form
. Therefore, the prime factors of q will also have a factor other then 2 or 5.
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Formula-
(i) =
The denominator is in the form of
Hence it is terminating.
(ii)
The denominator is in the form of
Hence it is terminating.
(iii)
The denominator does not satisfy the formula
Hence it is not terminating.
(iv)
The denominator satisfies the formula
Hence it is terminating.
(v)
The denominator does not satisfy the formula
Hence it is not terminating.
(vi)
The denominator satisfies the formila
Hence it is terminating.
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