How do we find that it is whether a terminating decimal or not without actul division?
Please explain this.......
Answers
Answer:
Figure out whether the denominator of the fraction has either 2 or 5 or both only as its prime factors, if it does then it is terminating.
Step-by-step explanation:
Let us take an example of 2/25
Prime factorization of denominator - 5*5
Since the denominator has only 5 as its prime factor.
It is a terminating decimal expansion
Take another example of 1/50
Prime factorization of denominator - 5*5*2
Since the denominator has only 5 or 2 as its prime factors.
It is a terminating decimal expansion
Take another example of 2/63
Prime factorization of denominator - 7*7
Since the denominator does not has 5 or 2 as its prime factors.
It is a non - terminating decimal expansion
Take another example of 2/150
Prime factorization of denominator - 5*5*2*3
Since the denominator does not has 5 or 2 only as its prime factors. (if 3 would not have been there,it would be a terminating decimal expansion)
It is a non - terminating decimal expansion