why is 3/17 rational, shouldn't it be irrational?

Question

since irrational numbers that never end and if you divide 3 by 17 im sure the numbers dont stop ? because i got to the thousandth and it didn't seem like it was going tno stop any time soon.

Answer 1

A rational number is a number that can be put in the form p / q where p and q are integers.
3 and 17 are integers
3 / 17 is rational

Answer 2

No, 3/17 is a rational number. It can be written as the fraction of two integers, so by definition it is rational.

Another definition of a rational number is a real number whose decimal terminates OR repeats. It's OK for rational numbers to have an endless decimal if it's REPEATING. 1/3 for example is 0.3333... with the "3"s going on forever.

If you keep extending the decimal part of 3/17, you'll notice that a certain block of digits keeps repeating itself. It's a really long block, but the first 16 digits do repeat:

3/17 = 0.1764705882352941 1764705882352941 1764705882352941 1764705882352941 ...

However, if you take a number like π or √2, you don't get a block that keeps repeating at any point. (And in case you're wondering: no, we don't have to keep checking digits out to infinity to know this for sure; we've been able to prove the irrationality of these numbers through other means.)

Answer 3

A rational number is a number that can be expressed exactly as an integer divided by a nonzero integer. By this definition, the fraction 3/17 is obviously rational. Terminating decimals, being expressible as the numerator without a decimal point and a denominator of 1 followed by as many zeroes as there are decimal places, are also rational.

Any repeating decimal can also be expressed as a ratio of integers, so is also a rational number. It can also be shown that a ratio of integers with a denominator n (assuming n is positive) can be expressed as a decimal with a period of repetition no greater than n-1. The fraction 3/17, when expressed as a decimal, has a period of repetition that reaches this maximum of 17-1, or 16.

Answer 4

rational number can be a fraction with terminating decimal

Or Repeating decimal. Like 1/3.

3/17 is a repeating decimal. =)

Answer 5

Any number which can be represented in the form of a/b where a and b are integers is rational. ex : 5 can be written as 5/1 , so 5 rational. 0.1 can be written as 1/10 , so 0.1 is rational . Where as sqrt(2) can not be represented in the form of a/b, so sqrt(2) is irrational.
Because 3/37 is in the form of a/b , it is rational.

Answer 6

If a number can be made into a fraction, then it's rational. That's the easy way to remember it. Numbers like pi can't be though, because they never repeat.