Bonus preview

Classifying numbers

The last PDF slide asks you to group numbers. Here is a quick preview: natural numbers are counting numbers; whole numbers add 0; integers add negative whole numbers. Rational numbers can be written as fractions. Irrational numbers cannot.

Class slide 88

How to answer questions

First simplify anything you can, such as √81 = 9.
Look for the most specific group: natural, whole, integer, rational, or irrational.
Remember: a number may belong to several groups. For example, 9 is natural, whole, integer, and rational.

Worked examples

−19 is an integer and rational. 1.2 = 6/5, so it is rational. √10 is irrational.

How to prepare

Draw nested circles: natural inside whole inside integer inside rational. Put irrational numbers outside those circles.

Watch out: Dots after a decimal do not prove it is irrational; you must know whether the digits repeat or follow a pattern.

Try it:

Classify √81 and −6/11.

I can do this

Show answer

√81 = 9, so it is natural, whole, integer, and rational. −6/11 is rational, but not an integer.

More practice · 3 questions

Try all three before you open the solutions.

Warm-up

Which groups include 0: natural, whole, integer, rational, or irrational?

Show solution

Using the counting-number definition of natural numbers in this guide, 0 is whole, integer, and rational because 0 = 0/1.

Practice

Classify √64 in every group it belongs to.

Show solution

First simplify: √64 = 8. Eight is natural, whole, integer, and rational because 8 = 8/1.

Challenge

Classify 0.125 and π as rational or irrational.

Show solution

0.125 is rational because it equals 1/8. π is irrational because it cannot be written as a fraction of two integers.