Check whether 75/455 is terminating or non-terminating decimal expansion.
Answers
Given :- Check whether 75/455 is terminating or non-terminating decimal expansion.
Answer :-
we know that,
- if Prime factor of denominator are 2, or 5 , or 2 and 5 both = fraction is a terminating decimal expansion .
- if prime factors are other than 2 or 5 = fraction is a non - terminating decimal expansion .
so,
→ 75/455
→ Denominator = 455
→ Prime factors of denominator = 5 * 7 * 13 .
as we can see that , prime factors are 5, 7 and 13 . or other than 2 or 5 . therefore, we can conclude that, (75/455) is a non - terminating decimal expansion .
Learn more :-
(3) निम्न के स्थानीय मान लिखिये-
(अ)43.24
(स)884.20
(ब) 534.34
(द) 178.34
https://brainly.in/question/37666224
SOLUTION
TO CHECK
Whether
is terminating or non-terminating decimal expansion.
CONCEPT TO BE IMPLEMENTED
A fraction is said to have terminating decimal expansion if prime factorisation of denominator give only 2 and 5 as prime factors
EVALUATION
Here the given fraction is
We simplify it as below
So denominator = 91
Now
91 = 7 × 13
Since the prime factorisation of denominator 455 contains prime factors 7 and 13 other than 2 and 5
So the given fraction does not have terminating decimal expansion
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