3.7 Extension Activity

Learn to classify numbers as rational or irrational and graph them on a number line.

Vocabulary irrational number real number

A decimal that is nonterminating with no repeating pattern is an irrational number. For example, = 1.4142135 . . ., which does not terminate or repeat.

The set of real numbers consists of the set of rational numbers and the set of irrational numbers.

By definition, any ratio of integers is a rational number. Remember

Example 1: Identifying Rational and Irrational Numbers Identify each number as rational or irrational. Justify your answer. A. 0.375 Because the number is already in decimal form, 0.375 is rational. B. 0.666666 … Because the decimal form is nonterminating and repeating, 0.6

Because its decimal form is nonterminating and repeating, is rational. Continued: Example 1 C. √ 49 √ 49 = 7 Write the number in decimal form Because its decimal form is nonterminating and repeating, is rational. √ 49 D. √ 11 √ 11 3.16624… Write the number in decimal form There is no pattern in the decimal form of . It is a nonterminating, nonrepeating decimal. So is irrational. √ 11

Identify each number as rational or irrational. Justify your answer. Check It Out Identify each number as rational or irrational. Justify your answer. E. √ 64 √ 64 = 8 Write the number in decimal form Because the decimal form is nonterminating and repeating, is rational. √ 64 1 4 F. 1 4 = 0.25 Write the number in decimal form 1 4 Because its decimal form is terminal, is rational.

Example 2: Graphing Rational and Irrational Numbers A. Graph the list of numbers on a number line. Then order the numbers from least to greatest. 8 4 √ 12 , 4 5 , -2.6, 7 , - , 1.4 -2.6, - 8 4 , 5 , 1.4, √ 7 12

Check It Out B. Name the two perfect squares that the square root lies between. Then graph the square root on a number line, and justify its placement. √ 66 8 and 9 Since 66 is closer to 64 than 81, is closer to than . √ 66 64