Question

Classify the following number. Select all that apply.

Answer 1

-3 is an integer and a rational number

Answer 2

Answers: Rational, Integer

A rational number is anything we can write as a ratio or fraction of two whole numbers. In this case, -3 = -3/1 is the fraction of -3 over 1. This is why -3 is rational. This means it is not irrational. The literal definition of "irrational" means "not rational", which contradicts the previous statement of it being rational.

An integer is any positive or negative whole number. The value 0 is included as well. So -3 is also an integer. Any integer is a rational number, but not the other way around (eg: 2/3 is rational but not an integer).

The set of whole numbers is usually defined in your book to be {0, 1, 2, 3, 4, ...} which is the set of positive numbers without any decimal or fractional parts. The value 0 is included. We see that -3 is not in this set. So -3 is not in the set of whole numbers.

The set of natural numbers is {1, 2, 3, 4, ...} which is essentially the set of whole numbers, but kick out 0. This set is also known as the set of counting numbers. Like before, we don't see -3 in here so -3 is not in the set of natural numbers.