Player #3 Name: 3 & ' 81 3 ( 27 3 $ 9 3 ) 3 * c) 3. d 3 I It jd 3

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1 Math 43 Preparation for Liberal Art Majors Handout 16 Exponents and Scientific Notation Activity A: Exponent game Remove the face cards from a standard deck of 52 cards In a group of 2 or 3 people, choose one person to be the dealer Dealer will deal out 2 cards Each person will try to make an expression with the highest value For example, suppose the dealer dealt a 2 of hearts and a 6 of spade A player can make the expression either 2 " or 6 $, and decide which will give the higher value Do this 10 times Note: please let the ace cards be 1 Player #1 Name: Player #2 Name: Player #3 Name: Correct Answer Who got the correct answer? Questions: 1 What did you notice? What was your strategy? Does the expression with the largest exponent give you the largest value? Or does the bigger base give you the bigger value? :096 4 " 4 & ' 4 ( 64 4 $ 16 4 ) 4, 2 4 Activity B: Exponent zero and negative exponents 1) Look at the tables below a) Complete the tables by filling in the missing values 4 * 256<54 ) 4 3 & ' 81 3 ( 27 3 $ 9 3 ) 3 * 3,) 2 ( 8 2 $ 4 2 ) 2 : b) What patterns do you notice? What do you notice about negative exponents and the exponent zero? Continue the tables to show more negative exponents, if needed c) 3 d 3 d 3 I z 4 3k 3 ± z 4 2 * 2,) It jd 3 2,$ 2,( z Page 1

2 Results : - exponent D's ' : -7 7 ] 17 1 base It 7 8 Otherwise 3,4 3 Ek 348/ , ; gy0

3 3 9 y 3 cubed sgfuek, q 81

4 Is : 7 ' > W 1 time / 7 times 2 's : for larger numbers : small bis " > bigsma

5 2) Rank the following numbers from smallest to largest What was your strategy? 10 ( 10,$ 10 " 10,/ 10 $ 3) Evaluate each Leave all answers in fraction form a) (,$ / I 7-2 b) 7,$ 7 * c) 7,$ + 7 *, ttg l +1 fat # f # Jet d) 2,),$ e) 7,$ 7,) f) 2,( or (2-1)-2 3 (z j2 zakd ( j2 2 4,),$ Activity C: Numbers in Scientific Notation 4) Each number in problems parts (a) - (e) is given in scientific notation For each number, answer the following: (i) Discuss if each number is bigger or less than 1 Decide if the number very big or very small? If the number is big, do you have a sense how big (is it in thousands, millions, etc?) If the number is small, do you have a sense how small (is it about a thousandth, millionth, etc?) (ii) What is each number in standard form? Examples of numbers in standard form are 350,000 or (iii) What observations can you make about numbers in scientific notation? eighty a) CCSF has about 8 10 ' students 80,000 thousand Standard form: Bigger or Less than 1? zeros b) The distance from Earth to the Sun is approximately / positive exam miles / Standard form: Bigger or Less than 1? o 93,000,000 Page 2

6 ' Scientific Notation : D D xlo or or " small " 0 I a '

7 " Ilya 8314Og Escapism ", " * /

8 EE 1-? II I }N st c ± s 's 's } F

9 oio#fo < < 10 < 103<106

10 c) One inch is equivalent to ,$ meters 254 Standard form: Bigger or Less than 1? d) The diameter of a human hair is approximately 15 10,)* meters 5 Standard form: Bigger or Less than 1? mi ( 5 e) The human body contains approximately is 7 10 )( cells Standard form: Tuuuuww Bigger or Less than 1? 70,000,000,000,000 5) What do you observe about the numbers in scientific notation? o A b X m Numbers in scientific notation are of the form: 3 4 X 10-3 PUZZLE time! In groups of 2 or 3, reassemble the 16 small squares to make a larger square Where edges touch, an integer computation problem will match its solution in scientific notation Activity D: Applications of Scientific Notation 6) The speed of light is approximately : miles per hour a) Express this number in standard form 6 Leonora 671,000,000 miles per hour b) If light travels : miles in one hour, then how many miles will it travel in 1 minute? 671,000, ,183,333 miles Peanut in miles miles Tin Page 3 83 c) If it takes light 83 minutes to reach the Earth from the Sun, what is the distance of the Sun from Earth? miles 11,183, ,820,666 miles

11 miles per hour mmfr mwi ho immi m6 omim Fetus may am ' ' # i aye

12 7) McDonald s has sold more than ; hamburgers a) How many hamburgers has McDonald s sold in standard form? b) If it were possible to eat a hamburger every minute of every day (ye, day and night!) without stopping, how many years would it take to eat ; hamburgers? 8) A red blood cell is approximately 8 10," meters long If you can line up 2 10 ' red blood cells, how long would that be in meters? Properties of Exponents: 1 What did you notice about the exponents when you multiply two numbers in scientific notation? Example: ( ) 2 What if you divide? ( )* > Example: $ )*? 3 What if you add or subtract? Example: ( ) vs ( ) Example: ( ) vs ( ) Page 4

13 Rulesfortxponentsa 1 (a±o ) ' a a a2a3 aa aaa2+3a5 an am + n gouldbec? mn T 7 bases match abkabtaabaaabbbabb Cab) ( ( a b) 3 a3b3 Cab)m Oprah ambm

14 ? in matching bases 3032 I undefined

15 52 ;# at f- 3 F9 :* at 3-2

16 Rates 1 what does 65 mph mean? 2 30 mph? miles per minute 3 30 mph? feet per hour

17 HOMEWORK 16 Part A: Evaluate each of the following WITHOUT using the calculator ALL answers need to be in FRACTIONS 1) 5,) 2) (05),) 3) 5,) 4) ) &,) 5) 5,$ 6) ( &,) 7) 5 * + 5,) 8) 5 $ 5,$ 9) 5 $ 5,$ 10) 2,) + 3,) 11) (2,) + 3,) ) $ 12) (10,) + 2,) ),) 13) (10,) 10,$ ) * 14) 2,( + 3,$ Page 5

18 Part B: Solve each problem 1) The national debt in the United States is now near 2 10 )( dollars and there are about : in the US If every person paid their fair share of the debt, approximately how much would that be per person? Write answer in both standard form and scientific notation 2) Geographers keep track of how many people live in different areas of the world They are especially interested in how the populations of certain area change The table below shows the population of different regions in 1985 and in 2005 Place 1985 Population 2005 Population Earth ; ; China ; ; India : ; United States : : a) How many more people inhabited Earth in 2005 than in 1985? b) In 2005, the Earth s population is how many times greater than China s? China s population is how many times greater than the United States? c) In 1985, India s population is what proportion of the world s (Earth s) population? What about in the year 2005? Page 6