sets of numbers. objective - to recognize different sets of numbers and to identify a domain. sets...
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SETS OFSETS OFNUMBERSNUMBERS
Objective - To recognize different sets of numbers and to identify a domain.
Sets of Numbers
Naturals - Natural counting numbers{ 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 & Irrationals
Real Numbers
Rationals IrrationalsAny number which can be written as a fraction
Non-terminating and non-repeating decimals which can’tbe written as fractions.Examples:
7
2.09
0 3.
71
100209
1009
2
13
4 7.943
97
4
Numbers which can be expressed in the form , where a and b are integers and b is not equal to 0, are call RATIONAL NUMBERS. Rational numbers may appear in different forms, but all of them can be written as a fraction in the form a over b.
RationalNumber
Form a
b
2
2
1
41
5
21
5
0 9.
9
10
0 6 6.
2
3
ba
Real Numbers
Rationals IrrationalsAny number which can be written as a fraction
Non-terminating and non-repeating decimals which can’tbe written as fractions.
Examples:
3141592. ...
2 1414213. ...
1212112111211112. ...
123456789101112. ...
Examples:
7
2.09
0 3.
71
13
100209
1009
2
Sets of Numbers Reals
Rationals Irrationals- any number whichcan be written as afraction.
2
3, 7, -0.4
Fractions/Decimals Integers
61
4 , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3...
Negative Integers Wholes…-3, -2, -1 0, 1, 2, 3...
Zero0
Naturals1, 2, 3...
- non-terminating and non-repeating decimals
3141592. ...
2
Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Naturals1, 2, 3...
Wholes0
Integers-3 -19
Rationals2
3
61
4
-2.65
Irrationals2
Reals
1, 2, 3...
0
-3 -19
Rationals2
3
61
4
-2.65
Irrationals2
Reals
1, 2, 3...
0
Integers-3 -19
Rationals2
3
61
4
-2.65
Irrationals2
Reals
Wholes
1, 2, 3...
0
Naturals1, 2, 3...
Wholes0
Integers-3 -19
Rationals2
3
61
4
-2.65
Irrationals2
Reals
Identify all of the sets to which each number belongs.(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) -6
2) 75
8
3) 14
4) 6
Integer, Rational, Real
Rational, Real
Natural, Whole, Integer, Rational, Real
Irrational, Real
Identify all of the sets to which each number belongs.(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) 0
2) - 2.03
3)
4)
Whole, Integer, Rational, Real
Rational, Real
Irrational, Real
Integer, Rational, Real
2 3
10
-5 50 10-10
{-8, -4, 1, 5, 8}
Graphing on Number Lines
• Name the set of numbers that is graphed.
{-8, -4, 1, 5, 8}
11
2
Graphing Real Numbers on a Number Line
Graph the following numbers on a number line.
31
12
5
30.4
-4 -3 -2 -1 0 1 2 3 4
3 5
30.4
C o m p are 3
8 an d
2
5.
Set up the problem as follows:
3
8 _ _ _ _
2
5
• Multiply the denominator on the left by the numerator on the right.
• Multiply the denominator on the right by the numerator on the left.
16
15 < 16 therefore, 3/8 is less than 2/5.
<
15 <