3. rational numbers filled in.notebook
September 19, 2016
1) Natural Numbers ( )
• Natural numbers are made up of all the positive integers and zero. = (0,1,2,3,4...)
2) Integers ( )
• Integers include both positive and negative whole numbers and also include zero. = (...­2, ­1, 0, 1, 2...)
• The asterisk (*) means to exclude zero from the set of integers. * = (...­2, ­1, 1, 2...)
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3. rational numbers filled in.notebook
3) Rational Numbers (
September 19, 2016
)
• A number is a rational number when it can be written in the form of a fraction: a b
where, a is an integer and b is an integer except zero. • Basically, rational numbers include both positive and negative whole numbers and positive and negative fractions. However, the denominator of a fraction cannot be zero. • Ex: 5, ­2, and 0.3 are all rational numbers because they can be expressed as fractions: 5 = , ­2 = , 0.3 = = 2
3. rational numbers filled in.notebook
September 19, 2016
How Are All of these Numbers Related?
A Venn Diagram Can Show Us! • The Natural Numbers ( ) are a subset of the Integers ( )
• The Integers ( ) are a subset of the Rational Numbers ( )
• The Venn Diagram below can help you visualize this:
(natural numbers)
(integers)
(rational numbers)
Place the following numbers in the Venn Diagram above: ­5, ­2, ­3 , ­0.5 , 0 , 1 , 5 4
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3. rational numbers filled in.notebook
September 19, 2016
• Natural Numbers are included within Integers and Integers are included within Rational Numbers
• The symbol means "included"
• Therefore, we can abbreviate and write: • The symbol means "element of"
• For instance, 1.5 is a rational number, but is not an integer. We can express this by writing: 1.5 and 1.5 4
3. rational numbers filled in.notebook
September 19, 2016
Summary 1) Natural Numbers ( ) = only positive whole numbers including 0. 2) Integers ( )= positive and negative whole numbers including 0. *
= exclude 0.
3) Rational Numbers ( )= positive and negative whole numbers and fractions. Denominator cannot be zero.
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