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Question:
Asked by Alby Last Modified
Answer 
- 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.
- 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.
1.) RATIONAL NUMBER: A number is called a rational number if the form p/q and q≠ 0 and ‘p ‘and ‘q’ should be integers. The decimal expansion can be:
a.) Terminating (i.e. the division will have remainder=0)
b.) Non-terminating (i.e. the division will not have remiander=0, it will never end ) but repeating (i.e. the quotient will happen in some pattern)
The number to be terminating, the factors of ‘q’ should be any powers of 2, 5 or both. Therefore ‘q’ can be of the form 2^m or 5^n or both and or 2^m * 5^n.
2.) NON-RATIONAL NUMBER: A number with decimal expansion as non-terminating and non-repeating.
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