Question

13 /80 is termating decimals or not

Answer 1

hey !!

here's the answer>>>

yes it is terminating as it contains 2 and 5 as it's factor

hope this helps u

Answer 2

aloha user!!

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in order find whether 13/ 80 has a terminating decimal or not we are going to write the prime factorization of 80 first. ( it should have 2  and 5 in prime factorization with power n or m being natural nos. )

$\frac{13}{(2)(2)(2)(2)(5)}$


it is not having any factor other than  2 and 5 so it has terminating decimal.

what if we had to find after how many decimal places it will end?

we will write the prime factorization first.

80 => 2 × 2 × 2 × 2 × 5 
multiply it by five (three times) so as to get 10000

13/80 => ( 13 × 5 × 5 × 5 ) / 2 × 2 × 2 × 2 × 5 × 5 × 5 ×5 )
13/80 => 1625 / 10000
13/80 => 0.1625

therefore it will end after 4 decimal places.

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hope it helps :^)