Real numbers include decimals, fractions, integers, rational numbers like fractions and repeating decimals, and irrational numbers like pi. They can be positive or negative, and are organized on a number line that extends infinitely in both directions. Real numbers are grouped into categories including counting numbers, whole numbers, integers, rational numbers, and irrational numbers.

1. Real numbers include all the numbers in our
numbering system – decimals, fractions,
negative, positive and even funny or odd
numbers like Pi or imaginary numbers whose
square would be less than zero (an example
would be -1 or ).
They are called real because they show the
value of something real.
Numbers are grouped together or organized
according to their type.

2. -3 -2 -1 0 1 2 3
-3.5 -1/2 0.75 2 1/2
This is a number line. All of the real numbers can be
placed on this line. The arrows tell you that the line can
go on forever in either direction. It can also include many
more numbers than what are shown here.

3. This is the first grouping of numbers in the real number
system called the counting or natural numbers. These
numbers are positive, whole numbers beginning with one
and not including zero.
1, 2, 3,
4, 5,…

4. Our second grouping of numbers are called the
whole numbers. They consist of the counting or
natural numbers with zero added.
0, 1, 2, 3, 4,…

5. The third group
of numbers are
called integers.
They include the
whole numbers
AND their
opposites or
negatives.
…-3, -2, -1, 0, 1, 2, 3, 4,…
Negative numbers are used in areas such as, temperature
(above/below zero), elevation (above/below sea level),
credits/debits, positive/negative electric charge.

6. The fourth
group of
numbers are
called
rational
numbers.
They are
fractions,
decimals
that repeat,
decimals
that end
and their
opposites.
-1/2
-3.5
0.75
7.12
9/2
-
5/3
0.33

7. Irrational
numbers
are
numbers
that cannot
be written
as
fractions
(i.e. cannot
be written
as a/b, with
b  0).
They are
sorted
outside the
other
circles.

Pi
3
Golden Ratio

eEuler’s
Number
99

8. 1, 2, 3, 4,…
Counting numbers,
also called natural
numbers are the
positive, whole
numbers without zero
that are used to count
0, 1, 2, 3, 4,…
Whole numbers are
counting or natural
numbers with zero
included
Integers are the whole
numbers with their opposites
-1/2
-3.5
0.75
7.12
9/2
-
5/3
Irrational
numbers are
numbers that
cannot be
written as
fractions
(cannot be
written as a/b,
with b  0).
They are
sorted outside
the other
circles.
3
Rational numbers are integers, common
fractions and their opposites without the
denominator equaling zero, including
decimals that repeat themselves or that
just end

Pi
Golden Ratio
eEuler’s
Number
99
…-3, -2, -1, 0, 1, 2, 3, 4,…
The Real Number System

9. Diameter means across

13. Blatner, D. (2011, October 2011 ). Joy of Pi. Retrieved from http://www.joyofpi.com/index.html