Download The Real Number System

The Real Number System
Gloria Kent
South Lenoir High School
7/8/2017
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The Real Number System
• The Real Number System is divided into
two categories: Rational and Irrational.
Rational Numbers: Numbers that can be written as a
ratio of two integers. THEY STOP OR REPEAT IN
DECIMAL FORM!
Irrational Numbers: Numbers, such as square root of
2 or , are not rational. THEY NEVER STOP, AND
THEY NEVER REPEAT IN DECIMAL FORM.
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The Real Number System
• Rational Numbers: Include integers, whole numbers,
natural numbers, and numbers written as the ratio of
two integers.
• Integers: {. . . – 3, – 2, – 1, 0, 1, 2, 3, . . .}
• Whole Numbers: {0, 1, 2, 3, . . .}
• Natural Numbers: {1, 2, 3, . . .}
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The Real Number System
Real Numbers
Rational Numbers
Irrational Numbers
1/2
-2
3
3
0
15%
2/3
3
4
-0.7
2
-5
2
1.456
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The Real Number System
Real Numbers
Rational Numbers
Irrational Numbers
Integers
1/2
3
-2
0
- 0.7
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15%
3
2/3
3
4
2
-5
2
1.456
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The Real Number System
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole
1/2
3
0
3
2/3
3
4
-2
- 0.7
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15%
2
-5
2
1.456
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The Real Number System
Real Numbers
Rational Numbers
1/2
Irrational Numbers
Integers
Whole
Natural
0 3
3
2/3
3
4
-2
- 0.7
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15%
2
-5
2
1.456
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DENSITY PROPERTY
• Between any two real numbers is another
real number. Ex: Between 1and 2, there is
an infinite amount of numbers such as 1.01,
1¼, 1.99, etc.
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So, When is a number NOT
REAL???
• When there is division by zero.
– Example:
35
0
• When you try to take the square root of a
negative number.
– Example:
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3
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Real Numbers
•
•
•
•
Simply Put
Real numbers can be placed on a number line.
Rational numbers are ratios of integers whose
values terminate or repeat as decimals.
Irrational numbers are ratios of integers whose
values do not terminate or repeat as decimals.
Perfect squares are rational numbers.
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• Non-perfect squares are irrational
numbers.
• *****Remember that the calculator rounds
up when necessary, making a number look
as if it does not repeat.
• *****Ex. 2/3=.66667 *****
• INTEGERS: {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}
• WHOLE #: {0, 1, 2,…}
• NATURAL #: {1, 2, 3, …}
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