naseeam
asked on
Why can any fraction whose denominator has only 2s and 5s in its prime factorization can be written as a terminating decimal?
Why can any fraction whose denominator has only 2s and 5s in its prime factorization can be written as a terminating decimal?
This is 7th grade math question. It's not a homework problem.
Thank you!
This is 7th grade math question. It's not a homework problem.
Thank you!
A denominator of 10^n has only 2s and 5s in its prime factorization.
ASKER CERTIFIED SOLUTION
membership
Create an account to see this answer
Signing up is free. No credit card required.
If this is a 7th grade problem, I assume that naseeam wants a very simple answer as first provided. ... Thinkpads_User
SOLUTION
membership
Create an account to see this answer
Signing up is free. No credit card required.
"Why can any fraction whose denominator has only 2s and 5s in its prime factorization can be written as a terminating decimal?"

To be perfectly correct you must define "fraction" a bit narrower.
9/3 terminates

To be perfectly correct you must define "fraction" a bit narrower.
9/3 terminates
3 does not have only 2s and 5s in its prime factorization, so whether 9/3 terminates is irrelevant.
"3 does not have only 2s and 5s in its prime factorization, so whether 9/3 terminates is irrelevant. "
true
But it is relvant when considering the converse (I know, that was not asked)
true
But it is relvant when considering the converse (I know, that was not asked)
SOLUTION
membership
Create an account to see this answer
Signing up is free. No credit card required.
SOLUTION
membership
Create an account to see this answer
Signing up is free. No credit card required.
All covering the same ground over and over again here.
.... Thinkpads_User
.... Thinkpads_User
SOLUTION
membership
Create an account to see this answer
Signing up is free. No credit card required.
... Thinkpads_User said
"All covering the same ground over and over again here." Not quite
you said
"Any number you can divide by 2 or divide by 5 terminates (does not repeat). . "
but that is not really an answer to the question asked (which was Why?
furthermore consider a number (you said ANY number so try 1/3)
(1/3)/2 = 0.16666666....
does not terminate. so at best you have to expand your answer a bit.
The other answers tried (and eventually did) answer the why?
.
"All covering the same ground over and over again here." Not quite
you said
"Any number you can divide by 2 or divide by 5 terminates (does not repeat). . "
but that is not really an answer to the question asked (which was Why?
furthermore consider a number (you said ANY number so try 1/3)
(1/3)/2 = 0.16666666....
does not terminate. so at best you have to expand your answer a bit.
The other answers tried (and eventually did) answer the why?
.
Touche. I meant and should have said any nonrepeating number divided by 2 or 5 will terminate and not repeat. Carelessness on my part.
... Thinkpads_User
... Thinkpads_User
.... Thinkpads_User