Can someone please explain this math problem to me?

Question

"Every fraction (rational number) has a corresponding decimal form that either terminates or repeats. For example,5/16 = 0.3125 (the decimal form terminates),and 4/11= 0.363636 . . . (the decimal form repeats). Investigate a number of fractions to determine which ones terminate and which ones repeat.(Hint: You can focus on the denominator; study the prime factorizations of several denominators

Answer 1

well, you will have to have a calculator handy for this and know that fractions are 2 numbers divided by each other.
first try this 1 divided by 9. U will get 0.1111111 next try 1/11 to get .09090909 note that when the denominator (number on the bottom) is an odd number that results in a number that repeats in the decimal form answer. So does 1/3, 1/7 but others like 1/5 stop at 0.2 . Now look at the denominator and notice that if it can be factored it would brake down to smaller numbers and if one of them is a repeating type then your answer will repeat.
Note that 1/7, 1/11, 1/13 repeat a group of numbers
1/7= 0.142857 142857 over and over. the(142857) part.
1/11 just repeates 09 to get .09090909
1/13= 0.076923076923076923 the pattern is 076923 over and over. 6/13 is just 6 X the pattern .461538 again and again. other numbers like 2, 4, 8, 10 when used in the denominator do not cause a repetition because they are made up of 2's and/or 5's that don't cause repetition.

Answer 2

hey.. thats pretty easy just divide random numbers by eachother...heres an example

6/13 = 0.4615 that terminates


6/18 = 0.333333 that repeats

So just come up with random fractions like that... divide them and it takes care of itself

Answer 3

Here are some basics:
1/4 = .25
1/3=.3333...
2/3=.66...
2/5=.4