Question

check whether 75/4555 is terminating or non-terminating decimal expansion​

Answer 1

Step-by-step explanation:

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

Answer 2

Given :- check whether 75/4555 is terminating or non-terminating decimal expansion ?

Solution :-

Concept used :- we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

so, writing 75/4555 in simplest fraction we get :-

→ 75/4555

→ 25 * 5 / 911 * 5

→ 25/911 .

now, checking prime factors of denominator we get,

→ 911 = 1 * 911 { since 911 is a prime number. }

since prime factors of denominator are other than 2 or 5 .

therefore, we can conclude that the (75/4555) is a non-terminating decimal expansion .

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