Sets of Real Numbers (0-2) Objective: Classify and use real numbers.

Sets of Real Numbers A number line can be used to show the sets of natural numbers, whole numbers, integers, and rational numbers. Values greater than 0, or positive numbers, are listed to the right of 0, and values less than 0, or negative numbers, are listed to the left of 0.

Sets of Real Numbers Number Set Description Examples Graph (If Possible) Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Counting Numbers 1, 2, 3, . . . Counting Numbers and Zero 0, 1, 2, 3, . . . Whole Numbers and their Opposites . . ., -3, -2, -1, 0, 1, 2, 3, . . . Numbers that can be expressed in the form a/b, where a and b are integers and b  0. Numbers that cannot be expressed as terminating or repeating decimals, or in the form a/b, where a and b are integers and b  0. Rational and Irrational Numbers Together All Numbers

Venn Diagram Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers

Example 1 Name the set or sets of numbers to which each real number belongs. = 11 Rational Number Natural Number Irrational Number Real Number Whole Number Real Number Integer Rational Number Real Number

Graphing Sets of Numbers To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line. The number that corresponds to a point on a number line is called the coordinate of that point. The rational numbers and the irrational numbers complete the number line.

Example 2 Graph each set of numbers on a number line. Then order the numbers from least to greatest.

Repeating Decimals Any repeating decimal can be written as a fraction. Write 0.8 as a fraction in simplest form. Step 1: Let N represent the repeating decimal. Since only one digit repeats, multiply each side by 10 (If two digits repeat multiply by 100, for three multiply by 1000, etc.). Simplify. Step 2: Subtract N from 10N to eliminate the part of the number that repeats. Divide each side by the number in front of N. Simplify. N = 0.888. . . 10(N) = 10(0.888. . .) 10N = 8.888. . . 10N = 8.888. . . -(N = 0.888. . .) 9N = 8 9 9

Example 3 Write 0.23 as a fraction in simplest form. N = 0.232323. . . 99 99