1. Sets of Numbers
Students will be able to distinguish between different sets of numbers.

2. Numbers and Variables
In mathematics, vocabulary words are very important. We need to be precise so we all know what we are talking about.
There are several different sets of numbers that we will be exploring:
These are natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.
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Algebra Review

3. Types of Numbers
The natural numbers (sometimes called counting numbers) consists of the numbers {1, 2, 3, . . .}
The whole numbers consists of the set of natural numbers plus 0, or {0, 1, 2, 3, }
The set of integers consists of the whole numbers and their opposites, or { , -2, -1, 0 1, 2, 3, }
There are other numbers on the number line as well as the integers. Numbers such as: ½, 3.8, ¾, -1.9 can also be represented on the number line.
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Algebra Review

4. Types of Numbers (cont.)
Any number that can be written as the quotient of two integers , where a and b are integers and b is not 0) is a rational number.
An irrational number is one that can’t be written this way.
Together the set of rational and the set of irrational numbers make up the set of real numbers.
Some examples of irrational numbers are: and
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Algebra Review

5. How are these Numbers Related?
Here is a diagram of how these numbers are related.
Real Numbers (R)
Rational Numbers (Q)
Integers (Z)
Irrational Numbers
Whole Numbers (W)
Natural Numbers (N)
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Algebra Review

6. Classify the Numbers
-2.5 5
Rational number, Real number
Natural number, Whole number, Integer, Rational number, Real number
Irrational number, Real number
Irrational number, Real
number
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Algebra Review

7. Graphing Numbers All real numbers can be graphed on a number line.
The number that corresponds to a point on a number line is called the coordinate of the point.
Each real number corresponds to exactly one point on a number line.
The point that corresponds to the number is called the graph of the number, and is indicated by a solid dot.
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Algebra Review

8. Graphing Numbers Graph each of these numbers on the same number line:
| | | | | | | |
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Algebra Review

9. Ordering Real Numbers
Put these numbers in order from smallest to largest number:
First, change all the numbers to their decimal equivalents:
Then put the numbers in order:
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Algebra Review

10. Ordering Real Numbers What is different if the numbers are negative?
Put these numbers in order from smallest to largest number:
First, change all the numbers to their decimal equivalents:
Then put the numbers in order:
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Algebra Review