Scientific Notation Chapter Questions

Transcription

1 Scientific Notation Chapter Questions 1. What is the purpose of scientific notation? 2. When would you use scientific notation? 3. How do you convert between standard form and scientific notation? 4. How do you compare numbers when they are written in scientific notation? 5. How do you multiply and divide numbers in scientific notation? 6. How do you add and subtract numbers in scientific notation?

2 Scientific Notation Chapter Problems Purpose of Scientific Notation 1. Express the following powers of ten in standard form: a = b = c = d = e = 2. Express the following answers as powers of 10. a x 10 5 = b x 10 6 = c x 10-8 = d x 10-7 = e x 10 3 = 3. Express the following powers of ten in standard form: a = b = c = d = e = 4. Express the following answers as powers of 10. a x 10 4 = b x = c x 10 8 = d x 10-9 = e x 10 2 = How to Write Numbers in Scientific Notation 5. Which of the following are correctly written in scientific notation? a. 3.0 x 10 5 b x 10 9 c x 10 3 d. 15 x 10-5 e. 5.6 x 10-8 f. 4 x 10 2 g x Write each number in scientific notation. a. 13,030,000

3 b. 418,000 c. 25,024,000 d. 4,500,000 e. 20,000 f. 870,000,000 g h i j k l Write each number in scientific notation. a. Lightest blue whale: 418,000 lb b. Thinnest glass: in. c. Lightest bird egg: oz. d. Diameter of thinnest copper wire: in. e. Mass of Earth s atmosphere: 5,700,000,000,000,000 tons f. Amount of gold in Earth s crust: 120,000,000,000,000 metric tons 8. Which of the following are correctly written in scientific notation? a. 0.5 x 10 4 b. 15 x 10 9 c x 10-7 d. 1 x 10 6 e x 10-4 f x 10-2 g x Write each number in scientific notation. a. 4,566,000 b. 17,000,300 c. 35,000 d. 1,078,000,000 e. 4,560,700 f. 943,000,000,000 g h i j k l Write each number in scientific notation. a. Mass of smallest insect, a parasitic wasp: g b. Speed of light: 300,000,000 m/sec c. Mass of a dust particle: kg

4 d. Distance from Earth to the Sun is approximately: 149,600,000 km e. Earth s circumference: 40,000,000 m f. Distance between the Sun and Neptune: 4,497,100,000 km Converting to Standard Form 11. Write each number in standard form. a. Temperature at the Sun s core: 1.55 x 10 6 K b. Lowest temperature ever in a lab: 2 x K c. Radius of the neon atom is about 3.5 x meters d. Radius of Earth s orbit: 1.5 x meters e. Avagadro s number: x f. Weight of a paper clip: 1.1 x 10-3 lb. 12. Write each number in standard form: a. 7.5 x 10 5 b x c x 10-8 d x 10 6 e. 3.0 x 10-6 f x 10 8 g x Write each number in standard form. a. Width of a human hair:7.5 x 10-5 meter b. Distance between Jupiter and the Sun: x c. Charge on a Proton/Electron: x C d. Faraday constant: x 10 4 e. Number of bits on a computer hard disk (as of 2010): 1 x GB f. Wavelength of green light: 5.5 x 10-7 m 14. Write each number in standard form: a x 10-4 b x 10 9 c. 1.0 x 10-5 d x 10 8 e x 10-5 f x 10 6 g x 10-3 Comparing Numbers in Scientific Notation 15. Place the appropriate inequality symbols between the following numbers: a. 9.5 x x 10 7 b x x 10 3

5 c x x 10 5 d. 1.0 x x 10-5 e x x 10-9 f x x g x x 10 4 h x x 10 8 i. 3.5 x x 10-6 j x x Order the following sets of numbers from least to greatest. a. 2.3 x x x x 10 4 b. 4.0 x x x x 10 5 c. 4.3 x x x x 10-4 d. 2.5 x x x x 10-9 e. 5.4 x x x x 10 4 f. 9.2 x x x x Place the appropriate inequality symbols between the following numbers: a. 3.2 x x 10 9 b x x 10 7 c x x 10 8 d. 3.0 x x 10-9 e x x 10-3 f x x g x x 10 6 h x x 10 4 i. 8.3 x x 10-8 j x x Order the following sets of numbers from least to greatest. a. 4.7 x x x x 10 4 b. 2.0 x x x x 10 3 c. 9.9 x x x x 10 6 d. 1.9 x x x x e. 9.3 x x x x 10 8 f. 5.5 x x x x 10-7 Multiplying and Dividing with Scientific Notation 19. Evaluate the following. Express the result in scientific notation. a. (3.0 x 10-5 )(2.0 x 10 9 )= b. (4.0 x 10 3 )(5.0 x 10 5 )= c. (6.0 x 10-5 )(3.0 x 10 8 )= d. (1.5 x 10 8 )(3.2 x 10-4 )= e. (2.7 x 10-3 )(1.1 x 10 8 )= f. (1.3 x 10-4 )(2.0 x 10-6 )=

6 g. (8.4 x 10 6 ) (2.0 x 10 3 )= h. (9.3 x 10 8 ) (3.0 x 10-2 )= i. (5.4 x ) (2.0 x 10 4 )= j. k. l. 7.35x 10 5 = 2.1x x x10 9= 3.6x x10 12= 20. A tiny space inside a computer chip has been measured to be 2.56 x 10-6 meters wide, 1.4 x 10-7 meters long, and 2.75 x 10-4 meters high. What is its volume? 21. In one year about 478 billion telephone calls were placed by 145 million United States telephone subscribers. What was the average number of calls placed per subscriber? 22. Evaluate the following. Express the result in scientific notation. a. (3.0 x 10-5 )(3.0 x 10 8 )= b. (4.0 x 10 2 )(4.0 x 10 7 )= c. (7.0 x 10-3 )(6.0 x 10 6 )= d. (1.2 x 10 7 )(2.2 x 10-3 )= e. (2.0 x 10-4 )(7.1 x 10 9 )= f. (4.4 x 10-7 )(3.0 x 10-3 )= g. (6.6 x 10 8 ) (2.0 x 10 4 )= h. (2.7 x 10 6 ) (3.0 x 10-4 )= i. (7.5 x ) (2.0 x 10 5 )= j. k. l. 6.6x x10 15= 5.4x x10 8= 4.8x x10 10= 23. A tiny space inside another computer chip has been measured to be 3.5 x 10-7 meters wide, 1.8 x 10-8 meters long, and 6.45 x 10-5 meters high. What is its volume? 24. The point on a pin has a diameter of approximately 1 x 10-4 meters. If a neon atom has a diameter of about 7.0 x meters, about how many neon atoms could fit across the diameter of the point of a pin? Adding and Subtracting with Scientific Notation 25. Evaluate the following. Express the result in scientific notation. a. (2.1 x 10 5 ) + (2.7 x 10 5 )= b. (3.7 x 10 8 ) + (4.6 x 10 8 )= c. (6.8 x 10-6 ) - (3.4 x 10-6 )= d. (6.1 x 10 6 ) + (3.5 x 10 7 )= e. (8.5 x ) - (1.5 x 10 9 )=

7 26. What is the difference between the mass of Earth (5.98 x kg) and the mass of Venus (4.87 x kg)? 27. What is the difference between the mass of Jupiter (1.90 x kg) and the mass of Saturn (5.69 x kg)? 28. Evaluate the following. Express the result in scientific notation. a. (5.8 x 10 9 ) + (3.1 x 10 9 )= b. (3.5 x 10 6 ) + (5.8 x 10 6 )= c. (7.5 x 10-4 ) - (4.2 x 10-4 )= d. (5.4 x 10 7 ) + (2.2 x 10 8 )= e. (6.5 x ) - (3.4 x )= 29. What is the difference between the mass of Mars (6.42 x kg)and the mass of Mercury (3.3 x kg)? 30. What is the difference between the mass of Earth (5.98 x kg) and the mass of Mars (6.42 x kg)?

8 1. a. 10 b. 100 c d e a b c d e a b c d e a b c d e A, E, F 6. a x 10 7 b x 10 5 c x 10 7 d. 4.5 x 10 6 e. 2 x 10 4 f. 8.7 x 10 8 g x 10-2 h x 10.5 i. 9.2 x 10 4 j x 10-3 k. 6 x 10 5 l x a x 105 b. 9.8 x 10-4 c x 10.2 d. 5 x 10 /4 e. 5.7 x f. 1.2 x C, D, E, G 9. a x 106 Answer Key

9 b x 10 7 c. 3.5 x 10 4 d x 10 9 e x 10 6 f x g x 10-4 h x 10-3 i x 10-7 j x k x 10-4 l x a x 10-6 b. 3 x 10 8 c x d x 10 8 e. 4 x 10 7 f x a b c d e f a b c d e f g a b c d e f a b c d e f g

10 a. < b. > c. < d. > e. > f. > g. < h. > i. > j. > 16. a. 7.8 x 10 2, 2.3 x 10 3, 1.3 x 10 4, 4.5 x 10 5 b. 7.0 x 10 5, 5.0 x 10 7, 4.0 x 10 9, 6.0 x c. 3.3 x 10-4, 7.5 x 10-2, 4.3 x 10 4, 1.9 x 10 6 d. 5.5 x 10-25, 2.5 x 10-12, 9.5 x 10-9, 8.2 x 10 2 e. 2.1 x 10 4, 3.2 x 10 4, 5.4 x 10 4, 9.9 x 10 4 f. 8.2 x 10-6, 9.2 x 10-6, 8.2 x 10-5, 9.2 x a. < b. < c. < d. > e. < f. > g. < h. > i. > j. < 18. a. 4.7 x 10 3, 6.7 x 10 4, 6.5 x 10 5, 8.9 x 10 7 b. 5.0 x 10 3, 3.0 x 10 6, 4.0 x 10 8, 2.0 x c. 1.8 x 10-7, 5.7 x 10-3, 9.9 x 10 5, 4.4 x 10 6 d. 4.5 x 10-23, 1.9 x 10-10, 3.6 x 10-6, 9.7 x 10 3 e. 5.0 x 10 8, 6.7 x 10 8, 8.9 x 10 8, 9.3 x 10 8 f. 2.7 x 10-7, 4.5 x 10-7, 5.5 x 10-7, 9.0 x a. 6 x 10 4 b. 2 x 10 9 c. 1 x 10 8 d. 4.8 x 10 4 e x 10 5 f. 2.6 x g. 4.2 x 10 3 h. 3.1 x i. 2.7 x 10 6 j. 3.5 x 10-3 k. 5 x 10-5 l. 6 x x 10-17

11 x a. 9 x 10 3 b. 1.6 x c. 4.2 x 10 4 d x 10 4 e x 10 6 f x 10-9 g. 3.3 x 10 4 h. 9 x 10 9 i x 10 7 j. 2 x k. 6 x 10-5 l. 6 x x x a. 4.8 x 10 5 b. 8.3 x 10 8 c. 3.4 x 10-6 d x 10 7 e x 10 10s x x a. 8.9 x 10 9 b. 9.3 x 10 6 c. 3.3 x 10-4 d x 10 8 e x x x 10 24