SN Starter A group of students are asked to express this number ( 00.003048 ) to three significant figures. Which of the following are correct? .003 .003050 3.048 x 103 3.05 x 10-3 .00305 d. and e. are both correct.

Conversions Converting From One System of Units to Another You will need a conversion factor like ( 1 meter = 3.28 ft). It can be used two ways: (1m/3.28ft) or ( 3.28ft/1m) Multiply your given dimension by the conversion factor to obtain the desired dimension. How many feet in 2 meters? 2m (3.28ft/m) = 6.56 feet How many meters in 10 feet? 10ft(1m/3.28ft) = 3.05 meters

Converting Areas To convert areas, you must square the conversion factor. Conversion factor: 1 inch = 2.54cm A page is 8.5 inches by 11 inches. What is the area in square centimeters? The area in square inches is 95 in2. So…… 95 in2 = __________cm2 95 in2(2.54cm/1 in)2 = 95(6.45 cm2) / (1 in2) = 613 cm2

Converting Volumes To convert volumes, you must cube the conversion factor. A cubic foot is how many cubic inches? Conversion factor: 1 foot = 12 inches 1 ft 3 ( 12 in/ 1 ft)3 = 1 ft 3 ( 123 in3/ 13 ft3) = 1728in3

Using S.I. Prefixes

Examples 12nm = 12 x 10-9 m Finished. Change 12nm to meters. n = x 10-9 so replace it: 12nm = 12 x 10-9 m Finished.

Examples 250g ( 1 kg/1x103 g) = .250 kg Change 250 grams to kilograms. 1 kg = 1x103 gram 250g ( 1 kg/1x103 g) = .250 kg

Scientific Notation If numbers are very large, like the mass of the Earth 5900000000000000000000000 kg Or very small like the mass of an electron : .000000000000000000000000000000911 kg then standard decimal notation is very cumbersome, so we use scientific notation.

Scientific Notation Example: 5.9 x 1024 Example: 6.2 x 10-4 A number in scientific notation has two parts: 1st part: a number between 1 and 10 2nd part: 10 to some power. Example: 5.9 x 1024 1024 Means move the decimal 24 places to the right. Example: 6.2 x 10-4 10-4 Means move the decimal 4 places to the left.

Examples – Put the number in Scientific Notation Answer: 345000 = 3.45 x 105 b. .00034 Answer: .00034 = 3.4 x 10-4

Multiplication and Division Rule Example xmxn = xm+n x2x3 = x2+3 = x5 xm/xn = xm-n x6/x2 = x6-2 = x4 (xm)n = xmn (x2)3 = x2×3 = x6 (xy)n = xnyn (xy)3 = x3y3 (x/y)n = xn/yn (x/y)2 = x2 / y2 x-n = 1/xn x-3 = 1/x3

Examples Simplify: (2 x 103)(4 x 106) = (2)(4) x 103(106) = 8 x 109

Significant Figures How to count the number of significant figures in a decimal number. Zeros Between other non-zero digits are significant. a. 50.3 has three significant figures b. 3.0025 has five significant figures

Significant Figures Zeros in front of nonzero digits are not significant: 0.892 has three significant figures 0.0008 has one significant figure

Significant Figures Zeros that are at the end of a decimal number are significant. 57.00 has four significant figures 2.000000 has seven significant figures At the end of a non-decimal number they are not. 5700 has two significant figures 2020 has three significant figures

Non-Decimal Numbers Major pain to try to figure out the significant figures – it depends on the number’s history. Don’t Use Them.

SN Practice Find the number of significant figures. 2.00450 .0034050 1450 0.02040 6 sf’s. 5 sf’s 3 sf’s 4 sf’s

Significant Figures After Division and Multiplication After performing the calculation, note the factor that has the least number of sig figs. Round the product or quotient to this number of digits. 3.22 X 2.1 = 6.762  6.8 36.5/3.414 = 10.691  10.7

Significant Figures Addition or subtraction with significant figures: The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. Ex: 97.3 + 5.85 = 103.15  103.2

Trig Review

Sine, Cosine, and Tangent H SO q SA sin q = SO / H cos q = SA / H tanq = SO / SA (SO)2 + (SA)2 =H2

Example: Find the length of side a and the angles q and f. 5 3 q a a2 + 32 = 52 so a2 = 25 – 9 = 16, or a = 4 4/5 = cosq, so q = cos-1(4/5) = 36.9 degrees f + q = 90-, so f = 90 – 36.9 = 53.1 degrees

Practice SN Express each of these in terms of a, b and c. 1. sin(f) = ____________ 2. cos(q) = __________ 3. sin(q) = _____________ 4. tan(f) = ___________

EXIT SN How could you figure out the how tall the flagpole is that cast this shadow?