4 Basic TermsWidthHypotenuseHeightHeightLengthBaseRight AngleArea of a Side= (length)(width) or (length)(height) or (height)(width)Volume of Rectangle= (length)(width)(height)Area=1/2 (Base)(Height)
5 Basic Units Length – meter (m) Mass – gram (g) Time – second (s) Volume – liter (L)Prefixes:Kilo (k) = x1000Centi (c) = /100Milli (m) = /1000
6 Basic Units of Measurement QuantityNameSymbolSI Base UnitDerived UnitLengthMeterm-AreaSquare MetersAm2VolumeCubic MetersVM3VelocityMeters per secondνm/sAccelerationMeters per second squaredam/s2ForceNewtonNKg m/s2J/mEnergyJouleJKg m2/s2N mMassGramgPowerWattWKg m2/s3J/s
8 Significant Figures Two Rules: If there is NO decimal point – start at the RIGHT and count, beginning with the first non-zero digit.Ex sig figssig figssig figsIf there IS a decimal point – start at the LEFT and count, beginning with the first non-zero digit.Ex sig figssig figssig figssig figs
9 Practice Sig Figs How many sig figs in each number? A) B) C)D) E) F) 93,000,000G) 93,000,003 H) 93,000,000. I)
10 Operations with Sig Figs Rule: Count the number of sig figs in each number you are multiplying or dividing. Use all numbers you have in calculations. The round answer to lowest number of sig figs in problem. Ex x 3.12 = calculator answer 4 s.f. 3 s.f. 6 s.f. So round to 3 s.f. Answer is 88.4 Ex / 3.12 = calculator answer 4 s.f. 3 s.f. 6 s.f. So round to 3 s.f. Answer is 9.08
11 More Operations with Sig Figs Rule: When adding or subtracting, the answer should have the same number of decimal places as that of the number with the least decimal. Ex is 0-4, so is 5-9 , so round down round up = =65.59 Remember: Decimal points must line up!
12 More Sig Fig Practice 0.00000313 78 +17 - .99 ,000-33,000.03=-3.1=- 17
13 Scientific NotationUse to express really Big and really small numbers.Rules:Only ONE digit to the left of the decimalX10 to however many places you had to move the decimal point.If you moved the decimal to the left, the power to positiveIf you moved the decimal to the right, the power is negative
14 Practice with Sci. Not.Put in Sci. Not: Put in regular numbers: 24327= 4.82 x 102= 73.54= 7.8 x 104= = 1.2 x 10-4= = 9.01 x 10-2=
15 Add/Subtract with Sci Not The exponents must be the same. Do what you need to do change one of the numbers to the other’s exponent. Then add/subtract the base numbers together and keep the exponent.Ex: x x 103 = ?Change 4.55 x 102 to x 103Then add = 4.225Add in x 103And the answer is x 103
16 Multiply/Divide with Sci Not First multiply/divide the base numbers together. Then for multiplication, add the exponents together. For division, subtract the exponents.Ex. (2.4 x 102)x(3.2x 103)2.4 x 3.2 = 7.68Add the exponents – = 5Giving the answer: 7.68 x 105If we were dividing:2.4/3.2 = 0.75Subtract exponents – 2 – 3 = -1Answer: 0.75 x (You would then move the decimal point to leave one digit to the left for 7.5 x 100 or just 7.5.)
17 Metric ConversionsStandard unit of distance is the meter. It is abbreviated m.For very small things, it may be more appropriate to use centimeters or even millimeters:1m = 100 centimeters (cm)1cm = 10 millimeters (mm)How many millimeters are in 1m?For very large distances, it may be more appropriate to use kilometers:1kilometer (km) = 1000mWhat would you measure with km? cm? mm? m?
18 Metric ConversionsStandard unit of mass is the gram. It is abbreviated g.For small amounts, you may want to use the milligram (mg) which is 1/1000th of a gram.For large amounts, you may want to use the kilogram (kg) which is 1000g.What would you want to measure in mg? Kg? g?
19 Solving for variablesAlways do the same thing to both sides of the equation and you will be fine.Ex. Density = mass/volume Solve for mass. Solve for volume.Ex. E = mc2 Solve for c.Ex. A + B = C A + C = D Solve for C.
20 Dimensional Analysis (or Canceling out) To convert from one type of unit to another type, we use dimensional analysis. For example, if we want to convert 55mph to km/h we just need to set the problem up correctly.55 miles x ft x 39 cm x m x 1 km =1 hour 1 mile ft cm m38 km = 38 kph1 hour