1. The Real Number System
Essential Question: -How do we classify numbers as rational or irrational?

2. Understanding Rational and Irrational
“Makes Sense”
“Doesn’t Make Sense”
Rational Numbers
Irrational Numbers
-Any number that can
be written as a fraction.
-Non-terminating and
non-repeating decimals.
fractions
-can’t be written as a
fraction.
wholes
integers
terminating
decimals
repeating
decimals

3. Sets of Numbers Naturals - Natural counting numbers. { 1, 2, 3… }
{ 1, 2, 3… }
Wholes - Natural counting numbers and zero.
{ 0, 1, 2, 3… }
Integers - Positive or negative natural numbers or zero.
{ … -3, -2, -1, 0, 1, 2, 3… }
Rationals - Any number which can be written as a fraction.
Irrationals - Any decimal number which can’t be written
as a fraction. A non-terminating and non-repeating decimal.
Reals - Rationals and irrationals.

4. …-3, -2, -1, 0, 1, 2, 3... …-3, -2, -1 Sets of Numbers Reals Rationals
Irrationals
- any number that
can be written as a
fraction.
- non-terminating
and
non-repeating
decimals
, 7, -0.4
Fractions/Decimals
Integers
, -0.32, - 2.1
…-3, -2, -1, 0, 1, 2, 3...
Negative Integers
Wholes
…-3, -2, -1
0, 1, 2, 3...
Zero
Naturals
1, 2, 3...

5. Sets of Numbers
This is a Venn Diagram that displays the following sets of numbers:
Naturals, Wholes, Integers, Rationals, Irrationals, and Reals.
Reals
Rationals
-2.65
Integers -3
-19
Wholes
Irrationals
Naturals
1, 2, 3...

6. Identify each number below as natural, whole,
integer, rational, irrational, or real. More than one
may apply.
Rational
, Real
Whole
, Integer
, Rational
, Real
Integer
, Rational
, Real
Irrational
, Real
Natural
,Whole
, Integer
, Rational
, Real

7. Identify each number below as natural, whole,
integer, rational, irrational, or real. More than one
may apply.
Rational
, Real
Integer
, Rational
, Real
Natural
,Whole
, Integer
, Rational
, Real
Integer
, Rational
, Real
Irrational
, Real