Using Scientific Notation
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1 LESSON 6 Using Scientific Notation EXAMPLE A Multiply: (.5 0 )( 0 5 ). Express the answer in scientific notation. Multiplication is commutative and associative. Rearrange the factors and group the coefficients and powers of 0. (.5 0 )( 0 5 ) 5 (.5.0)(0 0 5 ) Multiply the coefficients. Then multiply the powers of 0. (.5.0) 5 7 (0 0 5 ) Write the product in scientific notation (.5 0 )( 0 5 ) EXAMPLE B Divide: Express the answer in standard form..5 0 Divide the coefficients. Then divide the powers of TRY Express the quotient 9 0 in 0 4 standard form. Express the answer in standard form.. 0 5, , Domain : Expressions and Equations
2 EXAMPLE C Use a calculator to multiply: (. 0 5 )( ) Enter the factors. (. 0 5 )( ) Press ENTER. The calculator gives the product in scientific notation..47 is the coefficient. The number following e is the power of 0..47e (. 0 5 )( ) E EXAMPLE D Verify the product found in Example C by using a calculator to multiply the numbers in standard form. Write the numbers in standard form , ,000,000 Enter the factors. Press ENTER..47E 0,000 64,000, e DISCUSS 0000 X In Example C, the exponents are 5 and 7. Why is the exponent in the product, and not 5 7 5? Lesson 6: Using Scientific Notation 5
3 EXAMPLE E Divide: Express the quotient in scientific notation Divide the coefficients Divide the powers of Multiply the quotient of the coefficients and the quotient of the powers of This is not scientific notation. Write in scientific notation. Rewrite 0. so it is in scientific notation So, ( 0 ) (0) 5 0 (.4 04 ) (8 0 6 ) 5 0 CHECK Check the answer by dividing the numbers in scientific notation on a calculator. What does the calculator show as the quotient? 6 Domain : Expressions and Equations
4 read Problem Solving A spacecraft leaves Earth s orbit at a speed of km per day. To travel from Earth to Saturn, the craft needs to travel a total distance of km. How long will it take the spacecraft to reach Saturn? plan Write an equation to represent the problem. To find the time to reach Saturn, divide the distance the craft needs to travel by the speed of the craft. Let n equal the number of days. ( ) 4 ( ) 5 n solve Divide the coefficients: Divide the powers of 0: Set the quotient of the coefficients and the quotient of the powers of 0 as factors. 0 Write the expression in scientific notation. Solve for n. n 5 0 check Convert each number in scientific notation into standard form. Then divide using a calculator Perform the calculations on your calculator. The calculator shows. Does this match your answer? It will take days for the spacecraft to reach Saturn. Lesson 6: Using Scientific Notation 7
5 Express each product in scientific notation. Practice. (4 0 )( 0 ). ( 0 5 )(7 0 9 ). (5 0 )( 0 ) HINT If the product of the coefficients is 0 or greater, what do you need to do to change it to scientific notation? 4. ( )( 0 ) 5. (. 0 )( ) 6. ( )( ) Express each product in scientific notation and in standard form. 7. ( 0 4 )(8 0 ) 8. (4 0 7 )( ) 9. ( )( ) Express each quotient in scientific notation (5 0 5 ) 4 (4 0 6 ). (. 0 5 ) 4 (5 0 ) Express each quotient in scientific notation and in standard form (9 0 4 ) 4 ( 0 5 ) (8.4 0 ) 4 ( 0 ) Domain : Expressions and Equations
6 Express each product or quotient in scientific notation. Then check your answer with your calculator, explaining the calculator display. 6. ( )(. 0 7 ) 7. (9. 0 )( ) 8. ( ) 4 (.5 0 ) 9. (. 0 5 ) 4 (5.5 0 ) Choose the best answer. 0. Momentum can be calculated by multiplying mass and speed. Which is the momentum of an object with a mass of. 0 4 kg traveling at a speed of. 0 m/s? A kg m/s B kg m/s C kg m/s D kg m/s. A computer can perform instructions in a second. Which expression shows how long it would take to perform instructions? A seconds B seconds C seconds D seconds. WRITE MATH Salvador estimates that there are about grains of sand in a cubic centimeter of sand. He then estimates that there are about cubic centimeters of beach sand in the world. Explain the steps you would take to find how many grains of beach sand there are in the world.. DEMONSTRATE Experiment with your calculator to see when very small or very large numbers are converted to scientific notation. Why do you think the calculator is programmed to change the format for numbers at that size? Lesson 6: Using Scientific Notation 9
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