Real Numbers Graphic Organizer – Chart of the Number Sets

How it works

Filled in from the top, this real numbers graphic organizer shows how the first four sets of the real number system build on one another and where the irrational numbers stand apart.

Read the full guide

How the sets fit together

An integer such as 5 is also rational, because it can be written as 5/1. The irrational numbers are the real numbers that are left. So on the tick chart −3 gets two ticks, as an integer and as a rational number, and √2 gets one.

Simplify before you classify: √9 is 3, a natural number.
Books differ on 0. Many school courses start the natural numbers at 1 and add 0 for the whole numbers; say which your class uses.

Questions and answers

What are the sets of real numbers?

Natural numbers, whole numbers, integers, rational numbers and irrational numbers. Together the rational and the irrational numbers make up all the real numbers.

What is the difference between rational and irrational numbers?

A rational number can be written as a fraction of two integers, such as 3/4, with a denominator that is not zero. An irrational number cannot. Its decimal never ends and never repeats, as with π and √2.

Is 0 a rational number?

Yes. 0 can be written as 0/1, a fraction of two integers, so it is rational. It is also an integer.

Is a repeating decimal rational or irrational?

Rational. A decimal that ends, or that repeats the same digits forever, can be written as a fraction: 0.75 is 3/4 and 0.333… is 1/3.

All 9 organizers

The sets 2

Real numbers graphic organizer: the five sets Natural, whole, integers, rational and irrational down the side, with a box beside each for what the set includes and for examples. A line under the chart says how the sets fit together.
Sets inside sets: natural to real Five numbered boxes joined by arrows: natural numbers, whole numbers, integers, rational numbers, real numbers. Each set holds all of the one before it, so write what is new.

Sort and classify 5

Blank tick chart The same five columns of boxes with the number column left empty, for a list of your own.
Decimal test: ends, repeats or neither Three kinds of decimal down the side. Tick rational or irrational for each and write an example. Two to a page, with a cut line.
One number, every set Write one number in the middle, then list its sets, say how you know, rewrite it and place it on a number line.
Rational or irrational? T chart Two open columns for sorting numbers called out in class.
Which sets? Tick chart for ten numbers Ten numbers down the side, among them 0, −3, 0.75, π and the square root of 9, and a box under each set. Tick every set a number belongs to.

Sample and answer key 2

Answer key: which sets? The tick chart for ten numbers with every right box marked, the natural numbers starting at 1.
Sample real numbers organizer, filled in The opening chart with every box written in. Here the natural numbers start at 1 and the whole numbers add 0.