Which is a irrational number

A. 0.277277277 ...

B. 0.333 ...

C. 0.7

D. 3.14

D. Because since Pi never ends, it would be impossible to turn it into a fraction.

A) This is a repeating decimal which means it is possible to write it in the form p/q where p & q are integers and q is nonzero. So we can rule out choice A.

B) Similar to the answer choice above, we have another repeating decimal. So we can rule out choice B.

C) This is a terminating decimal. It does not go on forever. We can write this as a fraction (0.7 = 7/10). So we can rule out choice C.

D) This is also terminating so it seems like your teacher made a typo. What I'm thinking is that the 3.14 was meant to be a decimal that goes on forever without a pattern. This is a well known number called pi. I'm assuming that's what your teacher was going for.

So I'd go with choice D as the answer.