shankar.ashwin wrote:You get a terminating decimal only when the denominator contains factors of 2 or 5 or 2*5 (in any powers). All other numbers in the denominator produce recurring decimal.eg(3,5,7,9,11 etc)
128 is 2^7. So thats a terminating decimal.
All other options have other numbers in written in their base form (prime numbers raised to power something)
I will expand on this a bit because of how it is worded...
what shankar means to say is that it will terminate if and ONLY if the prime factorization is a combination of 2s and 5s ONLY. If you have ANY other prime factor in the answer other than a 2 or a 5, the fraction does not terminate...
i.e -
1/8 = 1/(2*2*2) = terminates
1/10 = 1/(2*5) = terminates
1/20 = 1/(2*2*5) = terminates
1/25 = 1/(5*5) = terminates
1/21 = 1/(3*7) = DOES NOT TERMINATE!!
1/60 = 1/(2*
3*2*5) = DOES NOT TERMINATE
30/60 = (3*2*5)/(2*3*2*5) = 3's cancel each other out, terminates!
or for a really tough one:
82.5/100 = 825/1000 = (11*3*5*5)/(5*5*5*2*2*2) = terminates! remember, ONLY the denominator matters!
even harder one:
39/130 = (3*13)/(2*5*13) = 13s cancel each other out, only 2s and 5s in denominator... terminates!
"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery
!
