4-5 Compute with Scientific Notation

Transcription

1 1. About fruit flies weigh pounds. How much does one fruit fly weigh? Write in scientific notation. Divide the weight of the fruit flies by the number of fruit flies to find the weight of one fruit fly. 3. ( ) + ( ) To add the numbers, rewrite one addend so that both addends have the same power of 10. Write as Use the distributive property to group the factors. Then add and Write the final answer in scientific notation. One fruit fly weighs about pounds. about lbs Evaluate each expression. Express the result in scientific notation. 2. ( ) ( ) To subtract the numbers, rewrite them so that they have the same power of 10. Write as Use the distributive property to group the factors. Then subtract 5.25 from Write the final answer in scientific notation Use the Associative Property to group the factors and powers of 10. Divide 8.25 by Subtract the exponents ( ) (24,650,000) Write 24,650,000 in scientific notation. 24,650,000 = To subtract the numbers, use the distributive property to group the factors. Then subtract from Write the final answer in scientific notation esolutions Manual - Powered by Cognero Page 1

2 ( ) Write 523 in scientific notation. 523 = To add the numbers, rewrite one addend so that both addends have the same power of 10. Write as Use the distributive property to group the factors. Then add 5.23 and 62. Write the final answer in scientific notation. 8. The equatorial circumference of Earth is about kilometers. The equatorial circumference of Jupiter is about 439,263.8 kilometers. About how many times greater is Jupiter s circumference than Earth s? Estimate the equatorial circumference of Jupiter and write in scientific notation. 439, ,000 or Divide the equatorial circumference of Jupiter by the equatorial circumference of Earth Use the Associative Property to group the factors and powers of 10. Divide 9.02 by 4.1. Subtract the exponents So, Jupiter's circumference is about 10 times greater than Earth's circumference. about 10 times greater 9. The United States has the most miles of roads in the world at about miles. Japan has about miles. How many more miles of roads does the United States have than Japan? Write in scientific notation. Subtract the number of miles of roads in Japan from the number of miles of roads in the United States to find how many more miles of roads the United States have than Japan. So, the United States has more miles of roads than Japan. about mi esolutions Manual - Powered by Cognero Page 2

3 10. The speed of light is about miles per second. It takes about 500 seconds for light to travel from the sun to Earth. What is the approximate distance between Earth and the sun? Write in scientific notation. Write 500 in scientific notation. 500 = Multiply the speed of light by the time it takes light to travel from the sun to Earth to find the approximate distance between the Earth and the sun. The distance between the Earth and the sun is about miles. 13. ( )(28,400) (0.042)( ) about mi Evaluate each expression. Express the result in scientific notation. 11. ( )( ) ( )( ) esolutions Manual - Powered by Cognero Page 3

4 ( ) + ( ) ,263,000 + ( ) esolutions Manual - Powered by Cognero Page 4

5 21. ( ) ( ) 25. ( )( ) ( ) 22, (0.0159)( ) ( )(56,200) The diameter of Mars is about meters. A standard table tennis ball is 0.04 meter in diameter. About how many times greater is the diameter of Mars than that of a table tennis ball? Write 0.04 in scientific notation = Divide the diameter of Mars by the diameter of a table tennis ball. 24. ( )( ) The diameter of Mars is about times greater than that of a table tennis ball. about times greater esolutions Manual - Powered by Cognero Page 5

6 28. The United States has a total area (including water) of about 9,826,630 square kilometers. Rhode Island is the smallest state with an area (including water) of about square kilometers. About how many times greater is the area of the United States than the area of Rhode Island? Estimate the total area of the United States and write in scientific notation. 9,826,630 10,000,000 or Divide the area of the United States by the area of Rhode Island. 30. Each minute, there are approximately flashes of lightning around the world. The air around a lightning bolt is heated to about degrees Fahrenheit, which is about five times hotter than the sun. Write each answer in scientific notation and in standard form. a. About how many flashes of lightning are there in a day? b. About how hot is the sun in degrees Fahrenheit? a. There are 1440 minutes in a day. Write 1440 in scientific notation = To find how many flashes of lightning there are in a day, multiply the number of flashes of lightning each minute by the number of minutes in a day. The area of the United States is about or 2500 times greater than the area of Rhode Island. about 2500 times greater 29. The Earth is kilometers from the Sun. Mercury is kilometers from the Sun. Find the difference in distances and express your answer in scientific notation. To find the difference in distances, subtract the numbers. There are or 8,640,000 flashes of lightning in a day. b. To find how hot the sun is, divide the temperature of the air around a lightning bolt by 5. In degrees Fahrenheit, the temperature of the sun is or 10,800. a ; 8,640,000 b ; 10, km esolutions Manual - Powered by Cognero Page 6

7 31. A music website recently announced that over songs have been downloaded. It also announced that it has registered users. Find the average number of downloads per user and express your answer in scientific notation. To find the average number of downloads per user, divide the number of songs by the number of users is close to the weight of the white rhinoceros. The white rhinoceros is about 10 times lighter than the right whale. b. Divide the weight of the blue whale by the weight of the African elephant. The blue whale is about or 20 times heavier than the African elephant downloads 32. Use Math Tools The table shows the weights of various marine and land animals. a. Which animal is about 10 times lighter than a right whale? b. About how many times heavier is the blue whale than the African elephant? c. Estimate the combined weight of the fin whale, right whale, and white rhinoceros. Write the combined weight in scientific notation and in standard form. c. Add the weights of the fin whale, right whale, and white rhinoceros. The estimated combined weight of the fin whale, right whale, and white rhinoceros is or 200,000 pounds. a. white rhinoceros b. 20 times c ; 200,000 a. Estimate the weight of the right whale Divide the weight of the right whale by 10. esolutions Manual - Powered by Cognero Page 7

8 33. The average width of a human hair is centimeter. If the cross section of the average hair is round, use the formula A = 3.14r 2 to find the approximate area of the cross section of a hair. Write your answer in scientific notation. The width of a human hair is equal to twice the radius. So, the radius of a human hair is centimeter. Substitute for r in the formula A = 3.14r A contractor is using a blend of two different types of sand for a new sand volleyball court. He is using cubic feet of sand that weighs 95 pounds per cubic foot and cubic feet of sand that weighs 88 pounds per cubic foot. How many tons of sand is being used for the volleyball court? To find the number of pounds of sand being used for the volleyball court, multiply the number of cubic feet of each type of sand by its weight per cubic foot. Find the sum of these products pounds of sand are being used for the volleyball court. There are 2000 pounds in 1 ton. To find the number of tons of sand, divide the number of pounds by Write 2000 in scientific notation = The area of the cross section of a hair is cm cm or 131 tons of sand are being used for the volleyball court. 131 tons esolutions Manual - Powered by Cognero Page 8

9 35. Evaluate each expression. Express the result in scientific notation esolutions Manual - Powered by Cognero Page 9

10 ( ,249) ( ,000) Identify Structure Write an addition expression and a subtraction expression, each with a value of Sample answers: Sample answers: ( ) + ( ); ( ) ( ) esolutions Manual - Powered by Cognero Page 10

11 44. Which One Doesn t Belong? Identify the expression that does not belong with the other three. Explain your reasoning does not belong = , while the three remaining expressions each equal does not belong = , while the three remaining expressions each equal Persevere with Problems There are about red blood cells in the average adult. A googol is About how many adults would it take to have a total of 1 googol red blood cells? To find how many adults it would take to have a total of 1 googol red blood cells, divide 1 googol by the number of red blood cells in the average adult. 46. Building on the Essential Question How does writing numbers in different ways help to make it easier to compute with very large or very small numbers? Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing. Sample answer: When you compute with very large or very small numbers written in standard notation, it can be difficult to keep track of the place value. Scientific notation is a concise way of expressing very large or very small numbers, making it easier to keep track of place value when computing. 47. Ariana is evaluating ( ) + ( ), as shown below. What should Ariana have done differently to evaluate the expression correctly? made both numbers have the same A power of 10 B subtracted the exponents C multiplied 8 4 instead of adding D made the last line She should have made both numbers have the same power of ten. She incorrectly added the exponents, which can only be done when applying the Product of Powers property. Choice A is the correct answer. It would take about adults to have a total of 1 googol red blood cells. A about adults esolutions Manual - Powered by Cognero Page 11

12 48. What is the value of ( )(1,600,000)? F G H J After its first year in business, a movie Web site announced that over 500,000,000 movies were downloaded by registered users. What is the average number of movies per user? A about movies B about 125 movies C movies D about 12.5 movies To find the average number of movies per user, divide the number of movies downloaded by the number of users. Choice J is the correct answer. J The average number of movies per user is or 125. Choice B is the correct answer. B 50. Short Response Earth is kilometers from the sun. Venus is 109 million kilometers from the sun. Find the difference in distances and express your answer in scientific notation. The difference in distances is kilometers km esolutions Manual - Powered by Cognero Page 12

13 Write an integer for each situation. Then identify its opposite C below zero Because it is below zero, the integer is 58. Its opposite is +58 or ; +58 or gallons per mile more than usual Because it is more than normal, the integer is +15 or 15. Its opposite is or 15; a withdrawl of $4500 Because it is a withdrawl, the integer is Its opposite is or ; or a scuba diver's descent of 50 feet Because it is a descent, the integer is 50. Its opposite is +50 or ; +50 or a bank deposit of $68.00 Because it is a deposit, the integer is +68 or 68. Its opposite is or 68; an airplane's ascent of 300 feet Because it is an ascent, the integer is +300 or 300. Its opposite is or 300; 300 Complete each expression = 18 + _ 18 5 = 18 + ( 5) _ ( 3) = 12 9 ( 3) = = 10 _ 12 = 10 ( 2) The volume of one cube is 5 3 cubic inches. What is the volume of 3.5 of these cubes? To find the volume of 3.5 of these cubes, multiply the volume of one cube by 3.5. The volume of 3.5 of these cubes is cubic inches in 3 esolutions Manual - Powered by Cognero Page 13

14 61. The speed of sound is approximately miles per hour. Write in standard form = The SR-71 Blackbird is more than 30 years old. It can fly at altitudes above feet. Is it more appropriate to report the altitude as feet or as inches? The measure feet is more appropriate. The number is very large so choosing a larger unit of measure is more meaningful ft Determine whether each equation is true or false. If the equation is false, explain why ( 4) = 12 This statement is true. The product of two integers with different signs is negative. true ( 3) = 5 This statement is true. The quotient of two integers with the same sign is positive. true = 6 This statement is false. The quotient of two integers with different signs is negative. 36 (6) = 6 false; 36 (6) = ( 11) = 132 This statement is true. The product of two integers with the same sign is positive. true ( 1) = 1 This statement is true. The product of two integers with the same sign is positive. true 64. This statement is false. false; esolutions Manual - Powered by Cognero Page 14