1-7 Compute with Scientific Notation
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1 Evaluate each expression. Express the result in scientific notation. 1. ( )( ) Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 3.9 and 2.3. Add the exponents. 2. ( )( ) Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 4.18 and 9. Add the exponents. 3. ( )( ) Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 9.75 and 8.4. Add the exponents. Write in scientific notation. esolutions Manual - Powered by Cognero Page 1
2 4. Use the Associative Property to group the factors and powers of 10. Divide 9.45 by 1.5. Subtract the exponents. 5. Use the Associative Property to group the factors and powers of 10. Divide 1.14 by 4.8. Subtract the exponents. 6. Use the Associative Property to group the factors and powers of 10. Divide 9 by 2.4. Subtract the exponents. esolutions Manual - Powered by Cognero Page 2
3 7. Neurons are cells in the nervous system that process and transmit information. An average neuron is about meter in diameter. A standard table tennis ball is 0.04 meter in diameter. About how many times as great is the diameter of a ball than a neuron? Write 0.04 meter in scientific notation: 0.04 = To find how many times greater the diameter of a table tennis ball is than the diameter of a neuron, divide. Use the Associative Property to group the factors and the powers of 10. Divide the factors. Subtract the exponents. The diameter of a table tennis ball is 8,000 times greater than the diameter of a neuron. Evaluate each expression. Express the result in scientific notation. 8. ( ) + ( ) To add the numbers, rewrite one addend so that both addends have the same power of 10. Use the Distributive Property to group the factors. Then add. Write the answer in scientific notation. 9. ( ) ( ) To subtract the numbers, rewrite them so that they have the same power of 10. Use the Distributive Property to group the factors. Then subtract. Write the answer in scientific notation. esolutions Manual - Powered by Cognero Page 3
4 10. ( ) + 590,000 Rewrite 590,000 in scientific notation: To add the numbers, rewrite one addend so that both addends have the same power of 10. Use the Distributive Property to group the factors. Then add. Write the answer in scientific notation ,100 ( ) Write 87,100 in scientific notation: To subtract the numbers, rewrite them so that they have the same power of 10. Use the Distributive Property to group the factors. Then subtract. Write the answer in scientific notation. esolutions Manual - Powered by Cognero Page 4
5 12. Persevere with Problems Central Park in New York City is rectangular in shape and measures approximately feet by feet. If one acre is equal to square feet, how many acres does Central Park cover? Round to the nearest hundredth. First find the approximate area of Central Park by multiplying feet and feet. Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 1.37 and Add the exponents. The area of Central Park in New York City is about square feet. Then, to find the number of acres Central Park covers, divide the area in square feet, , by the number of square feet in one acre, Use the Associative Property to group the factors and powers of 10. Divide by Subtract the exponents. Central Park covers about acres. esolutions Manual - Powered by Cognero Page 5
6 13. Find the Error Enrique is finding. Find his mistake and correct it. Sample answer: The Quotient of Powers property says to subtract exponents when dividing with the same base. The exponents are 6 and 2. Enrique subtracted positive 2 from 6 instead of negative 2. esolutions Manual - Powered by Cognero Page 6
7 14. Which One Doesn t Belong? Identify the expression that does not belong with the other three. Explain your reasoning. Look at each number ( )( ) = ( ) or (3.4)(4.2) = All the expressions except are equivalent. esolutions Manual - Powered by Cognero Page 7
8 15. Persevere with Problems A googol is the number 1 followed by 100 zeros. a. What is one googol written in scientific notation? b. How many times greater is a googol of meters than a nanometer? c. There are about red blood cells in the average adult. About how many adults would it take to have a total of 1 googol red blood cells? a. If a googol is a 1 followed by 100 zeros, then to put it into scientific notation the decimal would move 100 places to the left. So, a googol = b. Write each number in scientific notation. Then divide. googol of meters: nanometer: A googol of meters is or times greater than a nanometer. c. Divide a googol of red blood cells by the amount found in one adult. Adults have a total of red blood cells. esolutions Manual - Powered by Cognero Page 8
9 16. Model with Mathematics Write an addition expression and a subtraction expression, each with a value of Sample answers: First decide on two decimals that add to give you 2.4. So, = 2.4. In order for them to add in scientific notation and have a sum with a power of 10-3 both decimals must both be multiplied by For subtraction the two decimals must subtract to give me 2.4. So, = 2.4. In order for them to subtract in scientific notation and have a difference with a power of 10-3 both decimals must both be multiplied by Evaluate the expression. Express the result in scientific notation. 17. ( )( ) Use the Commutative and Associative Properties to group the factors and powers of 10. Multiply 3.7 and 1.2. Add the exponents. esolutions Manual - Powered by Cognero Page 9
10 18. Use the Associative Property to group the factors and powers of 10. Divide 4.64 by 2.9. Subtract the exponents. 19. Use the Associative Property to group the factors and powers of 10. Divide 3.24 by 8.1. Subtract the exponents. Write the answer in scientific notation. 20. ( ) + 2,400,000 Rewrite 2,400,000 in scientific notation: ( ). To add the numbers, rewrite one addend so that both addends have the same power of 10. Use the Distributive Property to group the factors. Then add. Write the answer in scientific notation. esolutions Manual - Powered by Cognero Page 10
11 21. ( ) + ( ) To add the numbers, rewrite one addend so that both addends have the same power of 10. Use the Distributive Property to group the factors. Then add. Write the answer in scientific notation. 22. ( ) 9,500 Rewrite 9,500 in scientific notation: To subtract the numbers, rewrite them so that they have the same power of 10. Use the Distributive Property to group the factors. Then subtract. Write the answer in scientific notation. 23. Persevere with Problems A circular swimming pool holds cubic inches of water. It is being filled at a rate of cubic inches per minute. About how long will it take to fill the swimming pool? To find how long it will take to fill the pool, divide the amount of water the pool will hold, cubic inches, by the rate at which it is filled, cubic inches per minute. Use the Associative Property to group the factors and the powers of 10. Divide 1.22 by 1.5. Subtract the exponents. It will take about 813 minutes to fill the pool. To change minutes to hours, divide by = It will take hours to fill the pool. esolutions Manual - Powered by Cognero Page 11
12 24. Financial Literacy In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about dollars. About how many times larger was the national debt in 2010 than in 2003? Write 14 trillion in scientific notation: 14 trillion = To find how many times greater the debt was in 2010 than in 2003, divide. Use the Associative Property to group the factors and the powers of 10. Divide the factors. Subtract the exponents. The national debt in 2010 was two times larger than the debt in There are approximately 45 hundred species of mammals on Earth and species of fish. Fill in each box to make a true statement. There are more species of than species of on Earth. The difference in the number of species is. In order to compare the number of species of fish and mammals, they must both be converted in to standard form. 45 hundred = 4500 species of mammals So, there are more species of fish than species of mammals on earth. To find the difference, first write the numbers in the same form. Subtract 4,500 from 28, ,000 4,500 = 23,500 The difference in the number of species is 23, Population density is a measure of how many people are living in a region. To calculate population density, divide the population of a region by the area in square miles. The table shows the approximate populations and areas of different countries. Sort the countries from least to greatest population density. esolutions Manual - Powered by Cognero Page 12
13 Which country has the greatest population density? To calculate population density, divide the population of a region by the area in square miles. Use the Associative Property to group the factors and the powers of 10. Divide the factors. Subtract the exponents. China's population density: Poland's population density: Sweden's population density: esolutions Manual - Powered by Cognero Page 13
14 United States' population density: Which country has the greatest population density? China 27. A cube measures 6.6 inches on each side. a. Find the area of one face of the cube. b. Find the volume of the cube. a. The area of one face of the cube is represented by the equation A = s 2, where s is the side length of the cube. The area of one face of the cube is (6.6) 2, or square inches. b. The volume of a cube is represented by the equation V = s 3, where s is the side length of the cube. The volume of the cube is (6.6) 3, or cubic inches. esolutions Manual - Powered by Cognero Page 14
15 28. Complete the table shown. esolutions Manual - Powered by Cognero Page 15
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