Ch5.5 Real Numbers & Their Properties

Ch5.5 Real Numbers & Their Properties

The union of the rational numbers and the irrational numbers is the set of real numbers.

Natural numbers are the number that we use for counting. {1, 2, 3, 4, 5….}

Whole numbers are includes o and the natural numbers. {0, 1, 2, 3, 4….}

Integers includes the whole numbers and the negatives of the natural numbers. {…,-3, -2, -1, 0, 1, 2, 3….}

Rational numbers are the set of all numbers that can be expressed as a quotient of two integers, with the denominator not 0. Rational numbers can be expressed as terminating or repeating decimals. {a/b | a and b are integers and b is not 0}

Irrational numbers are the set of all numbers whose decimal representations are neither terminating nor repeating. Irrational numbers cannot be expressed as a quotient of integers. {2, -3, π, -π2,…}

· Changing the order in which we subtract and divide real numbers can produce different answers.

Ex1. Consider the following set of numbers: -7, -34,0, 0.6, 5, π, 7.3, 81.

List the numbers in the set that are

A. natural numbers. B. whole numbers C. integers. D. rational numbers. E. irrational numbers. F. real numbers.

Ex2. Consider the following set of numbers: -9, -1.3, 0, 0.3, π2, 9, 10.

List the numbers in the set that are

A. natural numbers. B. whole numbers C. integers. D. rational numbers. E. irrational numbers. F. real numbers.

Ex3. Name the property illustrated:

a) 3∙7=7∙3 b) 4+7+6=4+(7+6) c) 23+5=6+25

d) 2+3+7=2+(7+3) e) 17+-17=0 f) 2∙1=2