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NAME ______________________________________________ DATE 5-2 Rational Numbers ____________ PERIOD _____ (Pages 205–209) 5 5 9 1 25 5 • The set of whole numbers is {0, 1, 2, 3, 4, 5, …}. Such numbers as , , and are also whole Sets of Numbers numbers because they can be written as a member of this set. • The set of integers is the set of whole numbers and their opposites. a b • The set of rational numbers consists of all numbers that can be expressed as , where a and b 1 3 are integers and b 0. The numbers and 5 are rational numbers. Some decimals are rational numbers. • Decimals either terminate (come to an end) or they go on forever. Every terminating decimal can be written as a fraction, so all terminating decimals are rational numbers. For example, 45 100 9 20 0.45 or . Types of Decimals • Repeating decimals can always be written as fractions, so repeating decimals are always rational numbers. You can use bar notation to indicate that some part of a decimal repeats forever, for example, 0.333… 0.3 . • Decimals that do not terminate and do not repeat cannot be written as fractions and are not rational numbers. Example Express 0.2 3 as a fraction in simplest form. Let N 0.232323…. Then 100N 23.232323…. 100N 23.232323… N 0.232323… Multiply N by 100 because two digits repeat. Subtract N from 100N to eliminate the repeating part. 99N 23 ⇒ 23 99 N To check this answer divide 23 by 99. Practice Express each decimal as a fraction or mixed number in simplest form. 1. 0.6 5 3. 0.1 2. 0.444... 4. 1.26 Name the set(s) of numbers to which each number belongs. 3 5. 6. 1280 8 3 8. 0.5 7. 2.5 Replace each ● with , , or to make a true sentence. 1 9. ● 0.3 3 10. 2 ● 2.25 6 12. ● 0.75 11. 1.8 ● 1.7 8 5 6 6 13. Standardized Test Practice Which number is the greatest, , , , or 10 4 ? 9 4 A 9 6 B 11 13 5 C 11 6 D 10 13 13. B 4 9 2. 5 33 3. 13 50 4. 1 5. rational 6. integer, rational 7. rational 8. rational 9. 10. 11. 12. 34 3 5 Glencoe/McGraw-Hill Answers: 1. © Glencoe Pre-Algebra