Question

which of the following must describe an irrational number?
1- a number with a nonterminating decimal expansion
2- a number with a nonrepeating decimal expansion
3- a number with a repeating or terminating decimal expansion
4- a number with a non repeating and nonterminating decimal expansion

Answer 1

not #1: 1.333333... = 4/3
not #2, since 1.345 is nonrepeating (but terminating)
not #3: see #1, or 1.3 = 13/10
so, #4.