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Q: What set of numbers contain nonrepeating and nonterminating decimals?

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Irrational numbers.

A nonterminating number does not end. An example is the fraction 1/3. When written as a decimal, it is a nonterminating number. Also pi is a nonterminating number. Some nonterminating numbers are repeating, some are nonrepeating. But they just don't end.

Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational

Whole numbers contain no fractional part as do decimals

Yes

Because they do not contain decimals

The quotient of 5 and negative 30 is both. Rational numbers and integers include many of the same numbers. Integers are positive and negative counting numbers, but rational numbers include nonrepeating decimals and fractions.

Integers are whole numbers that do not contain fractions or decimals

Decimals are numbers.

19 whole numbers, and infinitely many fractions and decimals

Terminating numbers are decimal representations of rational numbers. Nonterminating numbers may or may not be rational numbers.

Some decimals are. Counting numbers are a proper subset of decimals.

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