4-4 Scientific Notation

Transcription

1 Express each number in standard form Estimate each value using scientific notation kg ,500 Express each number in scientific notation. 4. 1,600, , kg is about kg kg ml ml is about ml ml 9. 18,900,435 cm 18,900,435 cm is about cm cm esolutions Manual - Powered by Cognero Page 1

2 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 measure is more appropriate. The number is very large, so choosing the larger unit of measure is more meaningful ; The number is very large so choosing a larger unit of measure is more meaningful. 11. Order , , , and 400 from least to greatest. 400 written in scientific notation is has an exponent of 2 so it is the least number. The other numbers have the same exponent, so the numbers can be ordered comparing the factors. 3.4 < 3.5 < 4, so < < The numbers in order from least to greatest are , , , , , , 400 Express each number in standard form ,062, , esolutions Manual - Powered by Cognero Page 2

3 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 centimeter is about centimeter cm pound pound is about pound lb esolutions Manual - Powered by Cognero Page 3

4 28. 56,300,001 miles 56,300,001 miles is about miles mi 29. The distance between Earth and the Moon is about kilometers. Estimate this distance using scientific notation The distance between Earth and the Moon is about kilometers 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. The measure 0.33 millimeter per day is more appropriate. The number meter per day is very small, so choosing a smaller unit of measure is more meaningful 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? The measure 219 milligrams is more appropriate. The number 219 milligrams is very small, so choosing a smaller unit of measure is more meaningful. 219 mg Order each set of numbers from least to greatest , , , Because two of the numbers have an exponent of 2, compare their factors. 2.4 < 2.45 So, is less than Because the other two numbers have an exponent of 2, compare their factors. 2.4 < 2.45 So, is less than The numbers in order from least to greatest are , , , , , , , 2805, , , written in scientific notation is Only two of the numbers have the same exponent of 4. Compare their factors < 3.2 So, is less than The rest of the numbers can be ordered using their exponents. The numbers in order from least to greatest are , 2805, , , , 2805, , , esolutions Manual - Powered by Cognero Page 4

5 , , , Because the exponents are different, they can be used to order the numbers. 3 < 4 < 5 < 6 The numbers in order from least to greatest are , , , List the states in the table from least to greatest production of maple syrup , , , ,562,301, , , 905,000 9,562,301 written in scientific notation is ,000 written in scientific notation is Only two of the numbers have the same exponent of 6. Compare their factors. 9.5 < So, is less than 9,562,301. The rest of the numbers can be ordered using their exponents. The numbers in order from least to greatest are , 905,000, , 9,562, , 905,000, , 9,562,301 First, compare the factors of the numbers with an exponent of < 3.79 < 9.65 So, < < Then compare the factors of the numbers with an exponent of < 1.89 So, < The amounts of syrup produced in order from least to greatest are , , , , The states in order from least to greatest production of maple syrup are New Hampshire, Wisconsin, New York, Maine, and Vermont. New Hampshire, Wisconsin, New York, Maine, Vermont esolutions Manual - Powered by Cognero Page 5

6 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. b. Convert the dimensions of the sheet of gold to meters. 1centimeter is 0.01 meter. So, centimeters is meters ,400 _ ,400 written in scientific notation is written in scientific notation is So, 35,400 = = _ written in scientific notation is Because the exponent 2 is greater than the exponent 3, > > So, the volume of the sheet of gold is a cm b. m 3 cubic centimeters Replace each _ with <, >, or = to make a true statement _ The two numbers have the same exponent. Compare their factors < 5.8 So, < < _ 5,000,000 5,000,000 written in scientific notation is Because the exponent 5 is less than the exponent 6, < 5,000,000. < ,000 _ ,000 written in scientific notation is Because the exponent 4 is greater than the exponent 3, 27,000 > > _ written in scientific notation is Because the exponent 5 is less than the exponent 4, < < esolutions Manual - Powered by Cognero Page 6

7 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. 45. 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? To find about how far the Moon travels in one orbit around Earth, find the number of hours in 27.3 days and multiply by its speed. There are 24 hours in a day = There are hours in 27.3 days. The population of Illinois is about people. b. Illinois; 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 combined population of the two states is about people. So, the Moon travels about kilometers in one orbit around Earth. about km 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. To find how long it would take light to travel from Earth to the Moon, divide the distance between Earth and the Moon by the speed of light. a. about people b. Illinois; 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 So, it would take 1.28 seconds for light to travel from Earth to the Moon s esolutions Manual - Powered by Cognero Page 7

8 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. To find the number of vehicles on U.S. 59 during one year, multiply the number of vehicles in one day by 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 and sum: So, the number of vehicles on U.S. 59 during one year is about To verify the solution using estimation, round 338,510 down to 300,000 and round 365 up to 400. difference: product: about quotient: 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. Each zero is a power of 10. googol: centillion: googol: ; centillion: esolutions Manual - Powered by Cognero Page 8

9 50. 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 the Florida. b. c. 3.8 million is easier to read and understand than the standard form (3,800,000) or scientific notation ( ) of the number. a ; is only about 40,000 people, which is not very many for the second largest city in Florida. b. 3,800,000 or 3.8 million c. 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 is twice as great as = 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 is greater than because the exponent of 3 is greater than the exponent of 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 Choice B is the correct answer. B ; = 300 and = 600 or esolutions Manual - Powered by Cognero Page 9

10 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 Choice G is the correct answer. 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 The weight of a fruit fly is about pound lb 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. 366,400 = The farm produces pounds of avocados 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? Because the exponent 18 is greater than the exponent 23, a molecule of penicillin has a greater mass. The difference between the two exponents is 5. So, the mass of a molecule of penicillin is 10 5 times greater than a molecule of insulin. penicillin; 10 5 times greater Find each product or quotient. Express using exponents. 58. a a 5 a (n 4 )(n 4 ) n x 2 (4x 3 ) 12x 5 esolutions Manual - Powered by Cognero Page 10

11 64. Financial Literacy Of Quincy s monthly paycheck, Use the table to write an expression that shows how many bushels of green beans were picked. Simplify the expression. 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? Write the fractions as decimals and then compare the decimals. = 0.28 = < 0.45 A greater fraction of Quincy's paycheck goes to paying his college loans. college loans g = 78 + g The expression 78 + g shows how many bushels of green beans were picked g 63. Translate eight times the product of six times a number, all divided by 2 into an algebraic expression. Then simplify the expression. Phrase: eight times the product of six times a number, all divided by 2 Expression: [8(6n)] 2 Write each expression using a positive exponent h 8 [8(6n)] 2; 24n esolutions Manual - Powered by Cognero Page 11

12 67. ( 5) 1 Write each expression using exponents = x (6 6 6) 6 (6 6 6) 6 = ( 7) esolutions Manual - Powered by Cognero Page 12

13 76. (2 2) (2 2) = esolutions Manual - Powered by Cognero Page 13