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Transcript
Name ___________________________________________________ Date __________________ Classifying Real Numbers A rational number is a number that can be written as the ratio of two integers. An irrational number cannot be written as the ratio of two integers. • The square root of any whole number that is not a perfect square is irrational. The cube root of any integer that is not a perfect cube is irrational. • The decimal form of an irrational number neither terminates nor repeats. Rational numbers and irrational numbers together form the set of real numbers. Real Numbers Rational Integer Whole −1 0 Natural −2 1 2 3 −3 1 2 Irrational − 23 3 7 2.25 2 −2π − 3 0.3 Example 1 π Classify each real number in as many ways as possible. Number Subset(s) — Reasoning a. √18 b. 0.33 c. −√ 4 Integer, Rational d. — 56 7 Natural, Whole, Integer, Rational e. √5 — — 3— Irrational 18 is not a perfect square. Rational 0.33 is a repeating decimal. — — −√4 is equal to −2. Irrational 56 7 — is equal to 8. 5 is not a perfect cube. Practice Check your answers at BigIdeasMath.com. Classify the real number in as many ways as possible. — 1. √ 17 48 6 4. — 1 5 2. — 3. 0.25 — 5. −√ 25 3— 6. √ 32 Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 7. A natural number is a whole number. 9. A natural number is negative. 11. A rational number is a real number. Copyright © Big Ideas Learning, LLC 8. An integer is a natural number. 10. A real number is an irrational number. 12. A whole number is an irrational number. Topic 3.6