Learning target: A number belongs to more than one category, but sometimes a question asks for its most specific classification.
STEP 01
Understand the categories
- Natural numbers: 1, 2, 3, … (this site starts natural numbers at 1).
- Whole numbers: 0 and the natural numbers.
- Integers: … −2, −1, 0, 1, 2, …
- Rational numbers: numbers that can be expressed as a ratio of integers with a nonzero denominator. Terminating and repeating decimals are rational.
- Irrational numbers: real numbers that cannot be expressed as ratios of integers, such as π and √2.
STEP 02
Choose the most specific label
Examples
- 5 → natural
- 0 → whole
- −4 → integer
- 0.75 → rational
- √3 → irrational
Although 5 is also whole, integer, and rational, “natural” is the most specific listed label.
STEP 03
Square roots require attention
√16 = 4 is natural, but √2 is irrational. Simplify before classifying.
Try it: Classify −√25 as specifically as possible.
−√25 = −5, a negative integer. The most specific label is integer.
Ready to check your understanding?
Try new practice questions with helpful feedback.