Multiply and Divide with Scientific Notation - Glencoe

1 600 Prerequisite SkillsMultiply and Divide with Scientific NotationMississippi Standard: Multiply and Divide numbers written in Scientific can use Scientific Notation to simplify computations with very large and/or very small Multiply numbers in Scientific Notation , regroup to Multiply the factors and Multiply the powers of ten. Then simplify. To Multiply the powers of ten, use of PowersMultiplication with Scientific NotationEvaluate the expression ( 102)( 101).( 102)( 101) ( )(102 101)Commutative and Associative Properties ( )(102 101) Multiply by 102 1 Product of Powers 103 Add the exponents. 1,000103 1,000 3,250 Move the decimal point 3 the expression ( 103)( 104).( 103)( 104) ( )(103 104)Commutative and Associative Properties ( )(103 104) Multiply by 103 4 Product of Powers 107 Add the exponents. 10,000,000107 10,000,000 67,200,000 Move the decimal point 7 of PowersWordsTo Multiply powers with the same base, add their 35 32 5or 37xa xb xa bTo Divide numbers in Scientific Notation , regroup to Divide the factors anddivide the powers of ten.

2 Then simplify. To Divide the powers of ten, use of PowersQuotient of PowersWordsTo Divide powers with the same base, subtract their 4483 48 3or 45 xxba xa b, x 0600-609 MAC2-PS-874046 5/9/08 12:08 PM Page 600 Prerequisite Skills601 ExercisesMultiply or Divide . Express using 1034. 2253 5. 7765 6. 110096 Evaluate each expression. Express the result in Scientific Notation and standard ( 105)( 102)8.( 104)( 103)9.( 102)( 102)10.( 103)( 102)11.( 103)( 101)12.( 102)( 106)13.( 105)( 103)14.( 104)( 105)15. 110038 16. 110025 17. 110059 18. 110034 19. 110057 20. 1100160 21. 110082 22. 1100181 table shows the 2007 salaries of six Major League Baseball players. About how many times greater is Alex Rodriguez s salary than Juan Castro s salary? Sun burns about 106tons of hydrogen per second. How much hydrogen does the Sun burn in one year?

3 (Hint:one year 107seconds) area of the Pacific Ocean is 107square miles. The area of the Atlantic Ocean is 107square miles. About how many times greater is the area of the Pacific Ocean than the Atlantic Ocean?2007 Major League Baseball SalariesPlayerJuan CastroCoco CrispNomar GarciaparraChipper JonesKazuo MatsuiAlex RodriguezSource:USA TodayTeamCincinnati RedsBoston Red SoxLos Angeles DodgersAtlanta BravesColorado RockiesNew York YankeesSalary(dollars) 1061. 23 1071. 5 107 Division with Scientific Notation Evaluate the expression 110036 . 110036 110063 Associative Property 110063 Divide by 106 3 Quotient of Powers 103 Subtract the exponents. 1,000103 1,000 4,500 Move the decimal point 3 MAC2-PS-874046 5/9/08 12:08 PM Page 601602 Prerequisite SkillsThe Density PropertyMississippi Standard:Develop a logical argument to demonstrate the denseness of rational the number line below.

4 Find another integer that lies between theintegers 2 and integers 1, 0, 1, and 2 all lie between 2 and 3 on the number the number line above, find a number that lies between 1 and 2. Theiraverage, 1 12 , is one number that lies between 1 and a Number Between Two Given NumbersFind a number that lies between 13 and 12 on the number line number would be their average. 12 13 12 12 26 36 Rewrite 13 and 12 with a common denominator. 12 56 Add the numerators. 152 rational number, 152 , lies between 13 and 12 .Find a number that lies between 7 and One number would be their average. 12 [ 7 ( )] 12 ( )Add 7 and rational number, , lies between 7 and process above of finding another number between any two given numberscan be continued indefinitely. This suggests the .density propertyYou can use the density property to solve real-world Property for Rational NumbersWordsBetween every pair of distinct rational numbers, there are infinitely many rational MAC2-PS-874046 5/9/08 12:08 PM Page 602 Prerequisite Skills603 ExercisesIdentify a number that lies between points Aand Bon each number a number that lies between each pair of and 76.

5 10 and 97. 34 and 18. 2 and 1 12 23 and 4 34 10. 5 and 4 13 11. 4 and and and For reading class, Dylan is recording the number of hours he reads each week. This week, Dylan needs to read between 1 12 and 2 hours. What is a possible time between 1 12 and 2 hours that Dylan can read? COUNTRY For cross-country practice, the coach told the runners they needed to run between 5 12 and 5 34 miles. Give a possible distance between 5 12 and 5 34 miles that a runner can the density property for rational numbers with severalexamples of your the Density PropertyBAKING Genevieve s grandmother gave her a family recipe for apple grandmother does not use an exact amount of sugar, but told Genevieve to use somewhere between 1 14 and 1 12 cups of sugar. If Genevieve wants to use an exact amount of sugar that is somewhere between 1 14 cups and 1 12 cups, how much sugar can she use?

6 One possible amount is their average. 12 1 14 1 12 12 1 14 1 24 Rename 12 as 24 . 12 2 34 Add the whole numbers and add the fractions. 12 141 Rewrite 2 43 as an improper fraction. 181 or 1 38 , Genevieve can use 1 38 cups of MAC2-PS-874046 5/9/08 12:08 PM Page 603604 Prerequisite SkillsIdentify PropertiesName the property shown by each statement.(7 3x) 2x 7 (3x 2x) Associative Property0 5a 0 Zero Property of MultiplicationAlgebraic PropertiesMississippi Standard:Apply algebraic properties in the properties in the table below. These properties can be applied when order in which numbers are added or multiplied does not change thesum or 7 7 6a b b a3 8 8 3a b b aThe way in which numbers are grouped when added or multiplied does notchange the sum or (2 7) 4 2 (7 4)(a b) c a (b c)(3 4) 5 3 (4 5)(a b) c a (b c)To Multiply a sum by a number, Multiply each addend by the numberoutside the (7 4) 2 7 2 4a(b c) ab ac(5 6)3 5 3 6 3(b c)a ba caThe sum of any number and 0 is the 0 7a 0 aThe product of any number and 0 is 0 0a 0 0 The product of any number and 1 is the 1 3a 1 aMultiplicative IdentityZero Property of MultiplicationAdditive IdentityDistributive PropertyAssociative PropertyCommutative PropertyUse Properties to Simplify ExpressionsSimplify each expression.

7 Justify each (x 13)4 (x 13) 4 (13 x)Commutative Property (4 13) xAssociative Property 17 xAdd 4 and MAC2-PS-874046 5/9/08 12:08 PM Page 604 Prerequisite Skills6056(x 7)6(x 7) 6(x) 6(7)Distributive Property 6x the property shown by each m m 18d 18d3.(7y 8) 10y 7y (8 10y) 1 (6a 7b) 3 6a 3 7b 0 0 Simplify each expression. Justify each (6 x) (6a) (6 n) (x 8) (4w) (x 2) 2y 11 (x 7) 7(2 3n) zebra can run up to 40 miles per hour. An elephant can run up to xmiles per hour. Write and simplify an expression to find how many more miles azebra will run in six hours than an PHONESS even friends have similar cell phone plans. The price of each plan is $x. Three of the seven friends pay an extra $4 per month for unlimitedtext messaging. Write and simplify an expression that represents the total cost ofthe seven Properties to Problem SolvingMUSEUMST hree friends are going to the science museum.

8 The cost of admission is $xeach. It will cost an additional $4 to view a movie on the 3-D screen. Write and simplify an expression that represents the total cost for the three cost of admission plus the movie can be represented by (x+ 4). Multiply this cost by the number of friends, 3(x+ 4).3(x 4) 3(x) 3(4)Distributive Property 3x , the total cost for the three friends is $3x $ to Example 5. A fourth friend will meet the group of friends at the museum but will not go to the movie. Write and simplify an expression that represents the total cost for the four cost for the fourth friend is $x. Add this to $3x $ 12 x 3x x 12 Commutative Property 4x , the total cost for the four friends is $4x $ MAC2-PS-874046 5/9/08 12:08 PM Page 605606 Prerequisite SkillsMake Predictions from Circle Graphs and HistogramsMississippi Standard:Use proportions, estimates, and percentages toconstruct, interpret, and make predictions about a population based onhistograms or circle graph representations of data from a can make predictions about a given set of data displayed in a circle graph or histogram.

9 Use percentages to make predictions about data displayed in a circle graph. Predict from a Circle GraphThe circle graph shows the results of a survey ofthe students in the 8th grade at Oakwood JuniorHigh. If there are 560 students at Oakwood JuniorHigh, how many would you predict to choosereality as their favorite type of television show?The section of the graph representing students whochose reality is 40% of the circle. So find 40% of find 40% of 560, you can use either 1 Write the percent as a of 560 40% 560 Write a multiplication expression. 560 Write 40% as a decimal. 2 Write the percent as a of 560 40% 560 Write a multiplication expression. 14000 5610 Write 40% as a fraction. Write 560 as 5160 . , about 224 students at Oakwood Junior High would choose reality as their favorite type of television Type of Television Show40%Reality28%Comedy16%Cartoon5%Drama 7%FictionPredict from a HistogramThe histogram shows the winning times of themen s 400-meter run in the summer Olympicsfrom 1896 to 2004.

10 Predict the range of speedsthat a runner finishing in first place is mostlikely to be in the next summer Olympics?Explain your bar at seconds is much higher thanthe others and represents the most winning , the winning speed of the runner in the nextsummer Olympics will most likely be in the second range. of WinnersTime (seconds)Summer Olympic Men s 400-Meter RunWinning Times, 1896 2004 Source: The World Almanac600-609 MAC2-PS-874046 5/9/08 12:08 PM Page 606 Prerequisite Skills607 ExercisesCARSFor Exercises 1 3, use the circle graph that shows the mostpopular luxury car a car dealership sold 50 luxury cars in March, predict howmany were a car dealership sold 250 luxury cars in January throughJune, predict how many were a parking garage has 85 luxury cars parked on a given day,predict how many are Exercises 4 and 5, use the circle graph thatshows the results of a survey of the favorite summertimeactivities of 7th grade students at Parson Junior High.