Hi guys! Can anyone help me with this?
"Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, .82, 5.096 are three terminating decimals. 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
I understand why it's not 1 (aka, eliminate answer "A" and "D" as correct) but why is the answer to this "B"? According to the back of the book: "Division by the number 4 must terminate: the remainder when dividing 4 must be 0, 1, 2, or 3, so the quotient must end with .0, .25, .5, or .75, respectively." I think I'm missing something obvious, but...I don't understand that last line! Can someone please explain this to me in a simpler way? How do I know it will never repeat, and will definitely terminate, for any number that I divide by 4, because of the ".0, .25, .5 or .75" ? If I test a bunch of numbers, is that what will happen and I just need to "know" that this is a rule that applies for 4? Or is there a rule I can use to scale out to other questions like this, where I'm not dealing with "4" but with some other number?
Thanks so much!
"Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, .82, 5.096 are three terminating decimals. 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
I understand why it's not 1 (aka, eliminate answer "A" and "D" as correct) but why is the answer to this "B"? According to the back of the book: "Division by the number 4 must terminate: the remainder when dividing 4 must be 0, 1, 2, or 3, so the quotient must end with .0, .25, .5, or .75, respectively." I think I'm missing something obvious, but...I don't understand that last line! Can someone please explain this to me in a simpler way? How do I know it will never repeat, and will definitely terminate, for any number that I divide by 4, because of the ".0, .25, .5 or .75" ? If I test a bunch of numbers, is that what will happen and I just need to "know" that this is a rule that applies for 4? Or is there a rule I can use to scale out to other questions like this, where I'm not dealing with "4" but with some other number?
Thanks so much!
