Types of Numbers
here are important sets of numbers you should know:
T Types of Numbers
Natural numbers: the numbers that occur ‘naturally’ in the world. { 1, 2, 3, …}
Whole numbers: the natural numbers, and 0. { 0, 1, 2, 3,…}
Integers: positive and negative natural numbers, and 0. {…-3, -2, -1, 0, 1, 2, 3,…}
a
Rational numbers: any number that can be written as a ratio where a and b are integers, b 0 .
b
2 7 0 1
Examples: ; 7 because it equals ; 0 because it equals ; 0.333 because it equals ; and
3 1 1 3
5667
5.667 because it equals .
1000
a
Irrational numbers: any number that can not be written as a ratio where a and b are integers.
b
Examples: any non-repeating, non-terminating decimals; 2 , and the special number e.
All of these are examples of what we call real numbers. The diagram below shows the relationship
between all these types of numbers.
Real numbers
Rational numbers
Integers
Whole numbers Irrational numbers
Natural numbers
1
Notice that does not fit any of these definitions. It is said to be an undefined expression.
0
Algebra 1 OBJ: Introduce types of numbers 1-3.A
Use the information from the previous page to answer the questions below.
Name all of the sets of numbers to which each number belongs:
1. -1 2. 1/3 3. 7 4. 0
Which is the most reasonable for each situation, whole numbers, integers, or rational
numbers?
5. Your shoe size. 6. The number of siblings you have
7. The number of quarts of paint you need to buy to paint a room.
8. The number of quarts of paint you use when you paint a room.
Is each statement true or false? If false, give a counterexample.
9. All integers are rational numbers.
10. All negative numbers are integers.
11. Every multiple of 3 is odd.
Algebra 1 OBJ: Introduce types of numbers 1-3.B
