Question

Check whether 75/455 is terminating or non-terminating decimal expansion.​

Answer 1

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

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Answer 2

SOLUTION

TO CHECK

Whether $\displaystyle \sf{ \frac{75}{455} }$

is terminating or non-terminating decimal expansion.

CONCEPT TO BE IMPLEMENTED

$\displaystyle \sf{Fraction = \frac{Numerator}{Denominator} }$

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

$\displaystyle \sf{ \frac{75}{455} }$

We simplify it as below

$\displaystyle \sf{ \frac{75}{455} }$

$\displaystyle \sf{ = \frac{15}{91} }$

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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