4-4 Scientific Notation
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1 Express each number in standard form ,500 Express each number in scientific notation. 4. 1,600, , Estimate each value using scientific notation kg Sample answer: kg ml Sample answer: ml 9. 18,900,435 cm Sample answer: cm 10. If you could walk at the rate of about 1 mile every 20 minutes without stopping, it would take about hours to walk from Columbus, Ohio, to Washington, D.C. Is it more appropriate to report the time as hours or minutes? Explain ; The number is very large so choosing a larger unit of measure is more meaningful. 11. Order , , , and 400 from least to greatest , , , 400 Express each number in standard form , ,062, esolutions Manual - Powered by Cognero Page 1
2 18. A dollar bill is approximately centimeter thick. Write in standard form It is estimated that more than s are sent each day around the world. Write in standard form. 171,000,000,000 Express each number in scientific notation , ,000, ,000, Estimate each value using scientific notation centimeter Sample answer: cm pound lb ,300,001 miles Sample answer: mi 29. The distance between Earth and the Moon is about kilometers. Estimate this distance using scientific notation. Sample answer: km 30. The usual growth rate of human hair is meter per day. Is it more appropriate to report the rate as meter per day or 0.33 millimeter per day? Explain your reasoning millimeter per day; The length is very small, so choosing a smaller unit of measure is more meaningful. 31. One ounce of a certain cheese has 219 milligrams of calcium. Is it more appropriate to include on the nutrition label that the cheese has kilogram of calcium or 219 milligrams of calcium? 219 mg Order each set of numbers from least to greatest , , , , , , , 2805, , , , 2805, , , esolutions Manual - Powered by Cognero Page 2
3 , , , , , , ,562,301, , , 905, , 905,000, , 9,562, List the states in the table from least to greatest production of maple syrup _ > _ 5,000,000 < ,000 _ > _ < New Hampshire, Wisconsin, New York, Maine, Vermont 37. A sheet of gold leaf is approximately centimeter thick. a. Write the value of the thickness as a decimal. b. Use the formula to find the volume in cubic meters of a sheet of gold that is 2 meters wide and 5 meters long. a cm b. m 3 Replace each _ with <, >, or = to make a true statement _ < ,400 _ = 44. Justify Conclusions A news article reported the population of Illinois to be 12,869,257 and the estimated population of Indiana to be a. Estimate the number of people living in Illinois. Express the number in scientific notation. b. Which state, Illinois or Indiana, has the greater population? Explain your reasoning. c. Estimate the combined population of the two states. Express the number in scientific notation. a. Sample answer: about people b. Illinois; Sample answer: Both numbers have a single digit times an integer power of 10. The power of 10 for the population of Illinois is greater than the power of 10 for the population of Indiana, so > c The Moon travels around Earth at a speed of about kilometers per hour. If the Moon orbits Earth every 27.3 days, about how far does it travel in one orbit around Earth? Sample answer: about km esolutions Manual - Powered by Cognero Page 3
4 46. The speed of light is about kilometers per second. The distance between Earth and the Moon is about kilometers. Find how long it would take for light to travel from Earth to the Moon s 47. In a recent year, route U.S. route 59 in the Houston area averaged approximately 338,510 vehicles per day. About how many vehicles was this during the entire year? Write the number in scientific notation. Verify your solution by using estimation. Sample answer: about Identify Structure Write two numbers in scientific notation with different exponents. Then find the sum, difference, product, and quotient of the two numbers. Write the answers in scientific notation. Sample answer: and ; sum: ; difference: ; product: ; quotient: Persevere with Problems A googol is a number that is 1 followed by 100 zeros. A centillion is a number that is 1 followed by 303 zeros. Write each of these numbers in scientific notation. googol: ; centillion: Justify Conclusions Miami is the second most populous city in Florida. a. Which number better describes the population of Miami: or ? Explain. b. Express Miami s population in another form. c. Which notation is best to use when describing population? Explain. a ; is only about 40,000 people, which is not very many for the second largest city in Florida. b. Sample answer: 3,800,000 or 3.8 million c. Sample answer: 3.8 million is easier to read and understand than the standard form (3,800,000) or scientific notation ( ) of the number. 51. Persevere with Problems Which number is twice as great as : , , or ? Explain ; = 300 and = 600 or Building on the Essential Question Your friend thinks is greater than because 7.8 > 6.5. Explain why your friend s reasoning is incorrect. Sample answer: is greater than because the exponent of 3 is greater than the exponent of The slowest land mammal is the three-toed sloth that moves 0.07 mile per hour. Which expression represents this number? A B C D B esolutions Manual - Powered by Cognero Page 4
5 54. The distance from Earth to the Sun is about miles. Which of the following represents this distance? F 9,600,000 mi G 96,000,000 mi H 960,000,000 mi J 9,600,000,000 mi G 55. Short Response The weight of a fruit fly is about pound. Estimate the weight of a fruit fly. Express the weight in the form of a single digit times an integer power of lb 59. (n 4 )(n 4 ) n x 2 (4x 3 ) x Use the table to write an expression that shows how many bushels of green beans were picked. Simplify the expression. 56. Short Response A 45-acre farm produces 366,400 tons of avocados per year. Write an expression, in scientific notation, for the number of pounds of avocados produced per year lb 57. Which type of molecule in the table has a greater mass? How many times greater is it than the other type? 78 + g 63. Translate eight times the product of six times a number, all divided by 2 into an algebraic expression. Then simplify the expression. [8(6n)] 2; 24n penicillin; 10 5 times greater Find each product or quotient. Express using exponents. 58. a a 5 a Financial Literacy Of Quincy s monthly paycheck, goes to pay his mortgage, and goes to pay his college loans. Does a greater fraction of his paycheck go to paying his mortgage or his college loans? college loans esolutions Manual - Powered by Cognero Page 5
6 Write each expression using a positive exponent h ( 5) (2 2) x ( 7) 4 Write each expression using exponents (6 6 6) esolutions Manual - Powered by Cognero Page 6
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