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Name _________________________________________________ Class _______________ Date _______________ Practice 1-3 Approximating Irrational Numbers 1-3 Approximating Irrational Numbers 1. On a number line, between which two consecutive whole numbers would 61 be located? ❍ A. 7 and 8 ❍ C. 6 and 7 ❍ B. 9 and 10 ❍ D. 8 and 9 2. The height of a painting is 90 ft. Between which two consecutive whole 90 ? numbers is ❍ A. 11 and 12 ❍ C. 10 and 11 ❍ B. 8 and 9 ❍ D. 9 and 10 3. Estimate 15 to the nearest tenth. Then locate 15 on a number line. 4. Estimate 37 to the nearest hundredth. Then locate 37 on a number line. 5. The area of a square poster is 31 in.2. Find the length of one side of the poster to the nearest tenth of an inch. 6. A tree is 16 feet tall. A wire runs from the top of the tree to a point 8 feet from its base. The wire is 320 feet long. Estimate the length of the wire to the nearest hundredth of a foot. 7. a) Writing On a number line, between which two consecutive whole numbers would 381 be located? ❍ A. 19 and 20 ❍ C. 18 and 19 ❍ B. 20 and 21 ❍ D. 21 and 22 b) Explain why it might be useful to approximate the value rather than use the exact value. 8. Mental Math The volume of displacement in an engine is which two consecutive whole numbers is 84 ? ❍ A. 8 and 9 ❍ C. 10 and 11 ❍ B. 11 and 12 ❍ D. 9 and 10 9. Error Analysis Diego incorrectly said that a) Estimate 84 L. Between 82 = 41. 82 to the nearest tenth. b) What was his likely error? ❍ A. He evaluated 82 instead of evaluating 2 ❍ B. He rounded incorrectly. 82 . ❍ C. He did not round. ❍ D. He evaluated the square root incorrectly. Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Practice 1-3 1 Homework G 10. a) Reasoning Estimate 35 to the nearest hundredth. b) Is the estimated value rational or irrational? Explain. 11. The formula d = 2s 2 gives the length, d, of a diagonal of a square with side length s. Each side of a square piece of wood is 33 cm long. You paint a stripe along the diagonal of the piece of wood. Estimate the length of the stripe to the nearest hundredth. 12. The length of a car is 162 ft. Will this car fit in a garage that measures 11 ft long? If not, what is the minimum length of a garage long enough for this car? 13. Estimate 150 to the nearest hundredth. 14. Challenge A square pool has a volume of 4,528 cubic feet and a depth of 8 feet. A couple builds a fence 3.5 feet high around the pool. How many square feet of fencing surround the pool? Round to the nearest tenth as needed. 15. Challenge The formula D = TR gives the voltage D (in volts) across an electrical circuit that uses power T (in watts) and has resistance R (in ohms). Electrical Circuits Circuit Power (watts) Resistance (ohms) A 51 5 B 50 9 C 57 6 a) Estimate the voltage across each of these circuits to the nearest hundredth of a volt. b) List the circuits in order of the voltages from least to greatest. Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Practice 1-3 2 Homework G ANSWER KEY Practice 1-3: Approximating Irrational Numbers 1. A 2. D 3. 3.9 4. 6.08 5. 5.6 in. 6. 17.89 ft 7. a) A b) Answers will vary 8. D 9. a) 9.1 b) A 10. a) 5.92 b) The estimated value is rational because it terminates and does not go on forever. 11. 46.67 cm 12. No, the car will not fit in the garage. The minimum length of a garage long enough for the car is 13 ft. 13. 12.25 14. 333.2 ft2 15. a) Circuit A: 15.97 volts Circuit B: 21.21 volts Circuit C: 18.49 volts b) A, C, B Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Practice 1-3 3 Answer Key G