Scientific Notation Scientist use special notation to express

Scientific Notation Scientist use special notation to express or very small numbers. very large Example I: 300, 000 m/sec can be written as… 3 x 108 m/sec Ex II: 1, 007, 000 sec can be written as… 1. 007 x 109 sec Ex III: 0. 000 000 004 76 m can be written as… 4. 76 x 10 -12 m

Converting Metric Measurements (PART 4 of Things to Know and Love) To convert, move the decimal place the number of stairs you step on in the direction you are traveling OR use dimensional analysis. kilo- 103 hecto- 102 deca- 101 Example: 3. 75 km = ? mm ? = 3, 750, 000 mm basic unit 1 deci- 10 -1 centi- 10 -2 milli- 10 -3

SIGNIFICANT FIGURES z Scientists indicate the precision of measurements by the number of digits they report = sig. figs. y. A value of 3. 52 g is more precise than a value of 3. 5 g z All known digits plus one estimated digit ** the equipment used for a measurement will determine the number of sig. figs.

Significant Figures Atlantic - Pacific Rule: Decimal Present: Count from the Pacific side Decimal Absent: Count from the Atlantic side Start counting at the first non-zero number and count until you reach the end of the number Ex. I: 3. 00700 Decimal Present… Pacific (left)… 6 sig. figs. Ex. II: 300, 700 Decimal Absent… Atlantic (right)… 4 sig. figs. (the last 2 zeros are PLACE HOLDERS)

REVIEW Determine how many significant figures are in each of the following measurements. 1) 0. 0034050 L ______ 2) 33. 600 m 5 (the first 3 zeros are PLACE HOLDERS) 5 ______ 5 3 ______ 10 ______ 3 ______ (the last 2 zeros are PLACE 3) 7500. 0 g 4) 47, 900 mm 5) 7, 000, 001 miles HOLDERS)

More practice… Round the following measurements off so that they each contain 3 significant figures. 7) 366. 2 L 366 L ______ 9, 050, 000 mg 8) 9, 047, 022 mg 12. 8 g ______ 1. 00 x 103 J 9) 12. 76 g Notice this one must ______ be in scientific notation to have 3 sig. figs. 10) 999. 9 J ______

Significant Figures in Calculations When multiplying and dividing, limit and round to the least number of significant figures in any of the factors. Example: 23. 0 x 432 x 19 = 188, 784 = 190, 000 The answer is expressed as 190, 000 or 1. 9 x 105 since 19 has only two sig. figs.

Significant Figures in Calculations When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers involved in the calculation. Example: 123. 25 + 46. 0 +86. 257 = 255. 507 = 255. 5 The answer is expressed as 255. 5 since 46. 0 has only one decimal place.

REVIEW Perform the prescribed operations. Round your answers to the proper # of sig. figs. 11. 4 m/s 11)36. 57 m / 3. 21 s = ______ 97. 6 g 12)41. 376 g + 13. 3 g + 42. 9 g=______ 76. 2 m 2 1. 0 m/s 2 ______ 60 V 13)5. 67 m x 13. 44 m 14)(5. 83 m/ 2. 67 s) /2. 1 s ______ From now on, we will round all our answers 15)9. 374 x 6 # of significant figures. to the Vcorrect ______

EXTRA REVIEW z. Using a calculator for EXPONONETS (EE, EXP or x 10 x button) y. Example 1: (5. 02 x 10 -3) x (6. 3369 x 105) = 3181. 1238 *put in correct sig figs = 3180 or 3. 18 x 103

Example 2 (use EE button!) z(2. 99 x 106) x (2. 334 x 10 -3) = = 6978. 66 • 3 sig figs • 6980

DIMENSIONAL ANALYSIS Ø How old are you in seconds? l Go from number of years to number of seconds. EX: 15 years old _____ seconds old. To do this, you need to use CONVERSION FACTORS (a ratio of equivalent values used to express the same quantity in different units)

Performing these conversions is a lot like going on a road trip.

ROAD TRIP!!! Let’s say you want to travel from Oracle Jct to Casa Grande. . . You must travel through Tucson… a two part trip.

Rule: You must stay on the roads & REMEMBER SIG FIGS!!!

DO NOT GO OFF ROAD! X

Rule: You need a map. Sometimes the map can be in your head. But, not at first. (show all work!!)

GIVEN INFORMATION 1 2 1 1 1 kildurkin = 18 gallons farkins = 1 kildurkin hogshead = 63 gallons barrel = 3. 3 bushels bushel = 8 gallons

Make a UNIT CONVERSION MAP Draw connections between the units in the conversion factors… (as you draw connections, check that conversion factor off the list) It’s kind of like a road map…

General Format. . . given X going to coming from =

hogshead gallons bushel barrel kildurkins farkins

Let’s calculate z. Convert 14 gallons to kildurkins

z. Convert 14 barrels to hogshead

z. Convert 3. 00 bushels to farkins

Now you try one. How many farkins is 3. 00 bushels? End Here hogshead gallons kildurkins farkins Start Here bushel barrel This will require 3 Conversions.

bushels 3. 00 bushels gallons kildurkins farkins 8. 0 gallons 1. 0 kildurkin 2. 0 farkins X X X 1. 0 bushel 18 gallons 1. 0 kildurkin = 2. 67 farkins

Wow! How Cool Is That!

Handout: Fun Factor Label z Handout z Piece of lined paper (landscape format) y. Front is web for Distance and back is for Vol. z Conversion Factors: change 10 -10 to 1 x 10 -10 z Let’s do league km m cm to start z You finish web, then do #3, 6, 7, 9 z Then do vol. web z Then finish questions #4, 5, 8, 10 z FINISH FOR HW