Number Types Examples

What are the five subsets of the real numbers?

These guys are the real deal. The real numbers are broken into two groups: the rational numbers and the irrational numbers. But the rational numbers include three other subsets as well: the natural numbers, whole numbers, and integers.

That means the real numbers include the natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Selfish much?

Which subsets of the real numbers include -5?

The integers include all whole numbers and their opposites. In other words, they include the negative numbers.

The integers are also included as a subset of the rational numbers, so our answer is technically integers and rational numbers.

The number is a nonterminating and nonrepeating decimal. Which subset of numbers is it included in?

"Nonterminating" means a decimal that never ends, like π. "Nonrepeating" means a decimal with no pattern of numbers that repeats on and on forever.

The rational numbers include only decimals that either eventually end or continue forever but with a repeating pattern, such as 0.5, 0.8925983 or 0.34343434…

Because does not end (nonterminating) and does not repeat a pattern (nonrepeating), it's an irrational number. Here are the first million digits of the square root of 7, in case you're curious.