Math, asked by legomibom10, 7 months ago

check whether 14588/625 a terminating decimal expansion .if yes,write it's decimal expansion.in mathematices​

Answers

Answered by RvChaudharY50
0

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.)

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