which of these is not included in the set of rational numbers? all integers, all whole numbers, all repeating decimals, or all non-terminating decimals

Answer: non-terminating decimals

Integers and whole numbers can be converted to fraction form. Example, the whole number 3 can be written as 3/1 which is rational. A rational number is any fraction of whole numbers (eg: 7/19). The denominator can never be zero.

All repeating decimals can be converted into a fraction. A number like 0.8888 with the 8s repeating forever converts to the fraction 8/9, which is rational

Non-terminating decimals are decimals that go on forever. If there is no pattern to the decimal sequence, then the decimals don't repeat and the number cannot be converted to a rational number. Something like pi = 3.14159 ... has no pattern to the decimal sequence. Therefore, a number like pi is irrational, which literally means "not rational", so numbers like pi aren't rational and are not part of the set of rational numbers.