1. TUESDAY 9-01 AND WEDNESDAY 9-02 SCIENTIFIC NOTATION, SI AND DIMENSIONAL ANALYSIS MRS. WILSON

2. THE HAND SIGNAL If I need your quiet attention, I’ll raise my hand and stop speaking. If you raise your hand and go quiet, we can get started quicker!

3. DAILY QUIZ 1-4 Obtain a calculator. Work by yourself. Work silently. Follow the LASA honor code. Flip over your purple sheet when you are finished.

4. OBJECTIVES 1.Understand and use correct math conventions in chemistry, including: - addition/subtraction of exponential numbers - multiplication/division of exponential numbers - SI quantities and prefixes 2. Convert quantities and rates using dimensional analysis. HOMEWORK 1.4 Homework – Daily Quiz 1-5 Next Class **Important: 1.4 Homework question #1 = it’s millidigs, not dillidigs

5. AGENDA 1.Daily Quiz 1-4 2. Powers of 10 + Video 3. Exponential Numbers and Sci. Notation 4. SI Units and Dimensional Analysis 5. Exit Ticket

6. POWERS OF 10 VIDEO https://www.youtube.com/watch?v=xmdIbp87KLg

7. POWERS OF 10 VIDEO https://www.youtube.com/watch?v=xmdIbp87KLg With your shoulder, discuss the answers to the following questions: 1.What does this video depict? 2.How does the content of the video apply to scientific quantities?

8. 1.4 MATH SKILLS (P. 9): EXPONENTIAL NUMBERS The numbers that we deal with in the laboratory are often very large or very small. Consequently, these numbers are expressed in scientific notation, using exponential numbers. These rules apply to the use of exponents: When n is a positive integer, the expression 10 n means “multiply 10 by itself n times”. Thus, 10 1 = 10 10 2 = 10 × 10 = 100 10 3 = 10 × 10 × 10 = 1,000 Examples: 2 × 10 1 = 2 × 10 = 20 2.62 × 10 2 = 2.62 × 100 = 262

9. 1.4 MATH SKILLS (P. 9): EXPONENTIAL NUMBERS The numbers that we deal with in the laboratory are often very large or very small. Consequently, these numbers are expressed in scientific notation, using exponential numbers. These rules apply to the use of exponents: When n is a negative integer, the expression 10 n means “multiply 1/10 by itself n times”. Thus, 10 -1 = 0.110 -2 = 0.1 × 0.1 = 0.01 10 -3 = 0.1 × 0.1 × 0.1 = 0.001etc. Example: 5.30 × 10 -1 = 5.30 × 0.1 = 0.530 8.1 × 10 -2 = 8.1 × 0.01 = 0.081

10. 1.4 MATH SKILLS (P. 9): EXPONENTIAL NUMBERS In scientific notation, all numbers are expressed as the product of a number (between 1 and 10) and a whole number power of 10. This is also called exponential notation. To express a number in scientific notation, do the following: 1. First express the numerical quantity between 1 and 10. Suggestion: Write “x 10 0” after the number. 2. Count the places that the decimal point was moved to obtain this number. If the decimal point has to be moved to the left, n is a positive integer; if the decimal point has to be moved to the right, n is a negative integer. Examples: 8162 requires the decimal to be moved 3 places to the left = 8.162 x 10 3 0.054 requires the decimal to be moved 2 places to the right = 5.4 x 10 -2

11. OR, YOU CAN LEARN THIS SONG… https://www.youtube.com/watch?v=AWof6knvQwE Follow the model, then Mix Pair Share the following…

12. MIX PAIR SHARE EXAMPLES Practice: Express the following numbers in scientific notation. 20,205 = 0.000192 = 5,800000,000 = ______________0.0000034 =______________ 40,230,000 =543.6 = 34.5 x 10 3 =0.004 x 10 -3 = 0.72 x 10 -6 =0.029 x 10 2 =

13. ADDITION AND SUBTRACTION OF EXPONENTIAL NUMBERS Before numbers in scientific notation can be added or subtracted, the exponents must be equal. Example: (5.4 x 10 3 ) + (6.0 x 10 2 ) = (5.4 x 10 3 ) + (0.60 x 10 3 ) So… (5.4 + 0.60) x 10 3 = 6.0 x 10 3

14. MIX PAIR SHARE PRACTICE (5.4 x 10 -8 ) + (6.6 x 10 -9 ) = (4.4 x 10 5 ) - (6.0 x 10 6 ) = (3.24 x 10 4 ) + (1.1 x 10 2 ) = (0.434 x 10 -3 ) - (6.0 x 10 -6 ) =

15. MULTIPLICATION AND DIVISION OF EXPONENTIAL NUMBERS A major advantage of scientific notation is that it simplifies the process of multiplication and division. When numbers are multiplied, exponents are added; when numbers are divided, exponents are subtracted. Examples:(3 x 10 4 )(2 x 10 2 ) = (3 X 2)(10 4+2 ) = 6 x 10 6 (3 x 10 4 )  (2 x 10 2 ) = (3  2)(10 4-2 )= 1.5 x 10 2 OR(3 x 10 4 ) = (3/2)(10 4-2 ) = 1.5 x 10 2 (2 x 10 2 )

16. Mix Pair Share: All answers should be left in scientific notation. (3.4 x 10 3 )(2.0 x 10 7 ) = _________ (5.4 x 10 2)  (2.7 x 10 4 ) =_____________ (4.6 x 10 1 )(6.7 x 10 4 ) = _________ (8.4 x 10 -3)  (4.0 x 10 5 ) = _____________ Combine everything you have learned and perform the following calculation. Write your answer in scientific notation. (3.24 x 10 8 )(14,000)/(3.5 x 10 -3 ) = _________________

17. PREFIXES USED FOR POWERS OF 10 / SI UNITS USED IN CHEMISTRY These are provided as a reference. Only some information on these two graphics need to be memorized since they’re the most commonly used.

18. DIMENSIONAL ANALYSIS The use of a conversion factor is often useful in doing more complex conversions. A conversion factor is simply the ratio between the two units of measurement. Examples:Give conversion factors for the following pairs of units. Kilograms and grams1000g = 1 kg so 1000g/kgor1 kg/1000g Liters and milliliters1 L = 1000 mL so1 L/1000mLor0.001 L/mL Meters and centimeters1 m = 100 cmso 100 cm/m or 0.01 m/cm Write conversion factors for the following pairs of units: Meters and micrometers Deciliters and picoliters Centigrams and megagrams

19. DIMENSIONAL ANALYSIS Often in chemistry, the measurements we need are not in convenient units. Not only are there metric units and prefixes to consider (distances in mm, cm, m, km..), there are American units (distances in feet, inches, miles…). When solving and communicating math problems, unit conversions are expressed in “dimensional analysis” – which we sometimes just call “train tracks” or “unit analysis.” The railroad tracks handles the basic algebra for us.

20. THINK PAIR SHARE: DIMENSIONAL ANALYSIS 1. Read the text and study the examples. Write notes on the page. Use your calculator. See if you can figure out the answers and how to cancel so you can obtain the correct unit for each answer. 2.With a partner, take turns summarizing the steps of how to solve using dimensional analysis. On page 13-14 you will find three worked examples and some steps for performing any dimensional analysis problem.

21. EXAMPLE 1 Let’s start with something basic. A wire is 1.3 feet long. How many centimeters is that? I know that 1 inch = 2.54 cm… and 12 inches = 1 foot. Setup your unit conversion railroad track so that units in the numerator (on top) will cancel with units in the denominator (on bottom).

22. EXAMPLE 2 Another example: A snail travels 13 feet / hour. How fast is this in m / sec? (12 inches = 1 foot; 1 inch = 2.54 cm)

23. EXAMPLE 3 Another example: Convert 30.0 in 2 to cm 2 For a problem like this you must square your conversion factor. So 1 in = 2.54 cm or 1 in 2 =6.45 cm 2

24. DIMENSIONAL ANALYSIS PRACTICE – I DO/WE DO/YOU DO Practice: Convert 555,000. square centimeters  square miles. Convert 1.00 square yard  square centimeters. Convert 30.0 m/s to km/hr Convert 459 ft/sec --> mi/hr

25. ADDITIONAL QUESTIONS: HARRY POTTER AND THE AMAZING UNIT ANALYSIS (YOU DO) (WHITEBOARDS) As Hagrid says, wizard money is very easy to understand. There are three coins: knuts, sickles and galleons. There are 29 knuts in one sickle and 17 sickles in one galleon. How many knuts in a galleon?

26. ADDITIONAL QUESTIONS: HARRY POTTER AND THE AMAZING UNIT ANALYSIS (YOU DO) (WHITEBOARDS) Ron has carefully hoarded every knut he’s found for 10 years and now he has three huge bags. He didn’t want to count every coin so he weighed the bags and found he had 75 pounds of knuts. One knut weighs 2 ounces. How much does he have in galleons? 16 oz. = 1 lb

27. ADDITIONAL QUESTIONS: HARRY POTTER AND THE AMAZING UNIT ANALYSIS (YOU DO) (WHITEBOARDS) Harry is practicing flying on his Firebolt. He does 10 laps around the Quidditch field in 18 minutes. One lap of the field is 700 meters (m). How fast is he going in kilometers (km) per hour? 1000 m = 1 km

28. ADDITIONAL QUESTIONS: HARRY POTTER AND THE AMAZING UNIT ANALYSIS (YOU DO) (WHITEBOARDS) One of the most important ingredients in Polyjuice Potion (used to make you look like someone else) is dried boomslang skin. As you know, boomslangs are very small which is why boomslang skin is so expensive. It takes 32 boomslangs to make 1 teaspoon (tsp.) of dried boomslang skin. The potion calls for ½ cup (c.) of skin. How many boomslangs have to give their lives for the recipe? 3 tsp. = 1 tablespoon (tbsp.)16 tbsp. = 1 cup

29. SEND A PROBLEM On a piece of paper, write your name, title it “Dimensional Analysis Practice”, and write three dimensional analysis “story” problems: a)One step b)Multi step c)Rate based Give them to a partner to write the work out for and solve! You must include the work, the answer, and the unit of your answer. Turn this in to the Class In Bin.

30. EXIT TICKET Describe three specific things you learned today and one question you have about today’s material. End of Class Procedure: Complete and turn in your exit ticket by yourself. You may not use any notes. Put your books etc. away. Wait for dismissal. Please, no phones! Clean up your table. When you are dismissed by me (not the bell), push in your chairs straight as you leave. Homework: 1.4 Homework. Daily Quiz 1-5 next class. NOTE: 1.4 Homework #1 – “millidigs” NOT “dillidigs”