Unit 2: Data Analysis Chapter 2
I.Units of Measurement A.SI System (Système International d'unités): modern version of the metric system. 1. The USA is the only country in the world which has not fully adopted the SI system. B.Base units: defined unit in a system of measurement, based off of an object or event in the physical world 1. SI contains seven base units
C.Derived units: combination of base units 1. Volume a. Units: cubic meters (m 3 ) or liter (L) b. Can also use varieties of the above units according to metric system (cm 3, ml, etc.) 2. Density a. Units: g/cm 3 or g/ml
Prefix Symbol Factor Scientific Notation giga G 1 000 000 000 10 9 mega M 1 000 000 10 6 kilo k 1000 10 3 hecto h 100 10 2 deca da 10 10 1 BASE 1 10 0 deci d 1/10 10-1 centi c 1/100 10-2 milli m 1/1000 10-3 micro μ 1/1 000 000 10-6 nano n 1/1 000 000 000 10-9 pico p 1/1 000 000 000 000 10-12
D.Temperature: a measure of average kinetic energy. 1. SI unit: Kelvin (K) 2. Instrument: thermometer 3. Zero Kelvin is absolute zero, the lowest possible temperature at which all motion in matter stops. a. 0 Kelvin = -273 Celsius.
4. Celsius ( C): the metric unit of temperature a. 0 C = freezing point of water (273 K) b. 100 C = boiling point of water (373 K) c. Celsius and Kelvin have the same size degrees, so it is easy to convert between the two units. d. K = C + 273 C = K - 273
II.Scientific Notation A.Often numbers are very large such as Avogadro s number (602 000 000 000 000 000 000 000), or very small such as the distance between salt particles (0.000 000 002 814 cm). 1. Scientific notation is a means in which we express these numbers in simpler terms. 2. Used mostly for numbers less than 0.001 or greater than 1000.
B.General form: M x 10 n 1. M is between 1 and 10 not including 10; n is any number 2. Example: a. 1 000 000 = 1 x 10 6 b. 602 000 000 000 000 000 000 000 = 6.02 x 10 23 c. 0.000 000 002 814 = 2.814 x 10-9 d. 0.000 000 35 = 3.5 x 10-7
C.Operations in Scientific Notation 1. Multiplication a. Multiply the M numbers, add the n numbers b. Example: (3 x 10 6 ) (2 x 10 3 ) = (2 x 10 3 ) (4 x 10-6 ) = 2. Division a. Divide the M numbers, subtract the n numbers b. Example: 6 x 10 6 / 2 x 10 4 = 4 x 10 3 / 2 x 10-3 =
3. Addition & Subtraction a. Make the n values the same by moving the decimal point. b. Add or subtract the M numbers and keep the common n. c. Example: (3.5 x 10 3 ) + (2.51 x 10 4 ) = (8.6 x 10 5 ) + (3.4 x 10 4 ) =
III.Dimensional Analysis A. Definition: method of problem-solving that focuses on units used to describe matter (SI units & the relationships between them) B.Utilizes equivalence statements such as 1 m=100 cm, 1 cm=10 mm, 1 dm 3 =1000 ml C.Equivalence statements can be rewritten into conversion factors: ratio of equivalent values used to to express the same quantity in different units 1 m 1 cm 1 dm 3 1. Examples: 100 cm 10 mm 1000 ml 2. Multiplying by these ratios is the same as multiplying by one 3. Ratio can be flipped (ex: 100 cm on top, 1 m on bottom) because it will still equal one
D. Steps in conversion (GUESS method) G: given -- write all information you are given U: unknown -- what are you looking for? E: equation -- what equation can/will you use? (use this when you do a problem -- not necessary for simply converting units) S: solve -- plug everything in, cancel your units, & do the math! S: solution -- rewrite your answer & circle it so I can find it easily :) don t forget to SIMPLIFY
E. Examples: 1. 1.56 km to m 2. 15,232 s to hours 3. 532 ml to dm 3 4. 500 mg to g F. Examples using derived units: 1. Procedure is same as before, you just may need more conversion factors 2. 15 km/h to m/s 3. 5670 ml/s to L/s
NOW... Practice Problems! p. 32: 12-14 p. 33: 15-16 p. 34: 17-18 p. 35: 19-21 p. 35: 22-24 p. 35: 25-28
IV. Reliability in Measurement A.Accuracy & Precision 1. Accuracy: refers to how close a measurement is to the actual quantity; related to the quality of the measuring instrument and the ability of the individual using it 2. Precision: refers to the uncertainty in measurement and/or how close a series of measurements are to one another; related to the quality of the measuring instrument and the measuring unit. a. Precision accuracy
B.Percent Error 1. Simple way of illustrating the accuracy of a measured or calculated value. 2. observed accepted % error = x 100% accepted 3. If you already know the number for error (sometimes given), use this: % error = error x 100% accepted
C.Significant Figures 1. A rounding technique that indicates precision of measurement 2. All known digits plus one estimated digit 3. Rules: a. Nonzero digits (1-9) are always significant (ex: 43 has 2 SF, 368 has 3, 95 has 2) b. All final zeroes after the decimal point are significant (ex: 8.750 has 4 SF) c. Zeroes between two other significant digits are significant. (ex: 3,065 has 4 SF, 5.03 has 3) d. Zeroes used solely for spacing the decimal point are not significant. (ex: 510 has 2 SF, 0.003 has 1) e. Counting numbers and defined constants have an infinite number of significant digits.
NOW... MORE Practice Problems! p. 38: 29-30 p. 39: 31-32 p. 42: 39-44
D.Operations with Significant Figures 1. Rounding a. Normal rounding rules b. If the digit to the immediate right of the last significant digit (that you are rounding to) is 5 & is followed by a nonzero digit, round up the last significant digit. Example: rounding to 3 sig figs 2.5351 = 2.54 c. If the digit to the immediate right of the last significant digit (that you are rounding to) is 5 & followed by 0, look at the last significant digit. If it is an odd digit, round it up. If it is an even digit, do not round up. Example: rounding to 3 sig figs 2.5350 = 2.54 2.5250 = 2.52
2. Addition and Subtraction a. Perform the operation (add or subtract) b. Round to least precise decimal point given (smallest amount of figures after decimal point) c. Examples: 745 m + 35.6 m + 220.35 m = 1000.95 m= 25.4 g - 21.35 g = 4.05 g =
3. Multiplication and Division a. Perform the operation (multiply or divide) b. Round to least number of significant figures given (smallest amount of sig figs) c. Examples: 5.600 cm x 3.95 cm x 4.3965 cm = 97.25058 cm 3 = 35.60 g / 25.235 cm 3 = 1.41073953 g/cm 3 =
NOW... PRACTICE PROBLEMS p. 41 #33-36 p. 42 #37-38 CHAPTER REVIEW Due next Thursday, October 15 (no block days next week) p. 49: Vocabulary (all) p. 50: Concept Mapping #51 p. 50: Mastering Concepts #52-68 p. 50: Mastering Problems #72-85 p. 53: Standardized Test Practice #1-9