STARTER Put this number in scientific notation. The mass of an electron is : .000000000000000000000000000000911 kg Put this number in scientific notation.

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

Calculators To enter a number in scientific notation into a calculator, the most common method is to use the EE button. Example: to enter 1.56 x 104 Press: 1.56(EE)4 Display: 1.56E4 In other words, E4 stands for “x 104 “

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

Summary For decimal numbers, start from the left and find the 1st nonzero digit. This digit and all others to the right are counted. 002.3400 has 5 sig. figs. For non-decimals, start from the left and find the 1st nonzero digit. This digit and all others to the right are counted until you get to only zeros which are not counted. 02304500 has 5 sig. figs

Non-Decimal Numbers Major pain to try to figure out the significant figures – it depends on the number’s history. Don’t Use Them. Use Scientific Notation to express any number to a desired amount of significant figures. Example: Express 234 to 4 sig. figs. 2.340 x 102

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

Percent Error and Difference

Accuracy vs. Precision

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 94 in2. So…… 94 in2 = __________cm2 94 in2(2.54cm/1 in)2 = 94(6.45 cm2) / (1 in2) = 606 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

Example Use the fact that c = x 10-2 A metal plate is 12.0cm by 4.0cm. What is the area in square meters? Use the fact that c = x 10-2 Area = (12.0cm)(4.0cm) = (12.0x10-2m)(4.0 x 10-2 m) = 4.8 x 10-3m2

Exit Physics uses the S.I. metric system, also known as the “mks” system. In this system, what are the base units for mass, time, and length?