How do we handle terminating decimals question like the one below?
If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?
(1) 90<r<100
(2) s=4
Now I read the explanation for the answer and it says any number divided by 4 is terminating decimal. How can you draw qucik conclusions for all the other divisors?
For eg.
Any number divided by :
1, has a terminating decimal
2, has a terminating decimal (0.5, 1)
3, does not have a terminating decimal (0.333..., 0.666..., 1)
4, has a terminating decimal (0.25, 0.5, 1)
5, has a terminating decimal (0.2, 0.4, 0.6, 0.8, 1)
6, may or may not have a terminating decimal (0.166..., 0.333..., 0.5, 0.666..., 0.833...)
Is this the right way to evaluate each divisor whether they will yield a terminating decimal? Or is there a set of rules that will be easier memorized than derived on the spot?
If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?
(1) 90<r<100
(2) s=4
Now I read the explanation for the answer and it says any number divided by 4 is terminating decimal. How can you draw qucik conclusions for all the other divisors?
For eg.
Any number divided by :
1, has a terminating decimal
2, has a terminating decimal (0.5, 1)
3, does not have a terminating decimal (0.333..., 0.666..., 1)
4, has a terminating decimal (0.25, 0.5, 1)
5, has a terminating decimal (0.2, 0.4, 0.6, 0.8, 1)
6, may or may not have a terminating decimal (0.166..., 0.333..., 0.5, 0.666..., 0.833...)
Is this the right way to evaluate each divisor whether they will yield a terminating decimal? Or is there a set of rules that will be easier memorized than derived on the spot?
