.333333 (.3 bar) irrational or rational

Question

Is .3333 rational or irrational?

I know that .333 (bar) can be converted to 1/3 which (a/b) makes the 1/3 rational so does the .333 get also classified as a rational number?

I was told that .3333 (bar) is irrational since it's repeating but 1/3 is rational but that makes no sense.

Answer 1

The prefix "ir" means "no" or "not" so the word "irrational" means "no ratio", or "not rational". 1/3 is rational, it is the ratio of 1 to 3. Therefore it is not irrational, meaning that 0.333repeating is also rational since it the decimal representation of 1/3.

Answer 2

It depends on the scale you're using. Take the distance between 2 stars; it's measured in "light-years"; which is at least 5.8 trillion miles. By using this length; .333333333333 is appropriate.

186292mps

864000 src/day

365 yr

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5.874904512*10^12 miles=light year

Answer 3