check whether 14588/625 a terminating decimal expansion .if yes,write it's decimal expansion.in mathematices
Answers
Question :- check whether 14588/625 a terminating decimal expansion .if yes, write it's decimal expansion in mathematices ?
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 .
Solution :-
in the given fraction (14588/625), denominator is 625 .
So,
Prime factors of 625 :-
→ 625 = 5 * 5 * 5 * 5
As we can see prime factors of denominator are 5 only .
Therefore, we can conclude that, given expansion is a terminating decimal expansion.
Now,
Decimal expansion :-
→ (14588/625)
→ (14588 * 16) / (625 * 16)
→ (233408 / 10000)
→ 23.3408 (Ans.)