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Chapter 2: Measurement and Calculations Key concepts: Differentiate between accuracy and precision Apply principles of measurement and significant figures Identify and use the 7 base SI units Name and apply units of measure Perform unit conversions Calculate density Calculate percent error A. Accuracy vs. Precision ACCURACY - How close you are to the correct __________ measurement or calculation based on the standard value. PRECISION - How close your measurements are to __________ EACH OTHER The density of aluminum is 2.78 g/cm3. Bob calculates the density three times and gets 2.75, 2.79 and 2.77. AVG: 2.77 ACCURATE AND PRECISE Mary calculates the density three times and gets 4.66, 4.67, and 4.65 AVG: 4.66 PRECISE BUT NOT ACCURATE Holden calculates the density three times and gets 10.25, 6.87, and 1.25 AVG: 6.12 NIETHER ACCURATE NOR PRECISE Franz calculates the density three times and gets 2.90, 1.95, 3.44 AVG: 2.76 ACCURATE BUT NOT PRECISE B. Measurement Measurement Something with magnitude, size or ___________ amount. Unit ________ - Compares what is measured to a defined size. Metric - Standard system of measure using ________ base 10. SI ________ - The international system of measure that uses only BASE metric units B. Measurement Quantitative - Measurements having numbers or ___________ size. Qualitative - Measurement having subjective ___________ descriptions Examples: 20 ml of water QUANTITATIVE The reaction bubbles QUALITATIVE Uma Thurman is blonde QUALITATIVE 17 g/ml QUANTITATIVE Bulldogs are #1 QUALITATIVE C. Significant figures Significant figures indicate the accuracy of the measuring instrument. 2.35 cm Last digit is ESTIMATED Not possible to estimate 2.3514584; can only estimate between graduations C. Significant figures Consider the following: What’s the estimate? This ruler isn’t as accurate as the previous. C. Significant figures RULE EXAMPLE All nonzero digits and zeros between those digits are significant 1 458 g Leading zeros with decimal points are NOT significant; Ending zeros ARE significant with decimal 0.0005 kg Ending zeros left of the decimal point may or may not be significant. Indication needed. 15 000 kg 40.7 m 10 150.01 mm 0.01008 m 1 701.10 L 0.00140500 m 15 000. kg 1.50E4 kg 1.500E4 kg NO. OF SIG FIGS 4 3 7 1 4 6 6 2 5 3 4 Scientific notation is always in sig fig form C. Significant figures ADDITION AND SUBTRACTION Answer has as many DECIMAL POINTS as the part with the LEAST decimals. 5.44 – 2.6106 = 2.8294 2.83 -13.4 2.4 – 15.82 = -13.42 2.099 + 0.05681 = 2.15581 2.156 0.258 + .1 = 0.358 0.4 C. Significant figures MULTIPLICATION AND DIVISION Answer can only contain as many SIG FIGS as the part with the LEAST sig figs 8.15 x 6 = 50 48.9 0.250 / 0.87 = 0.29 0.2873563218 1.2 x 1010 = 1200 1212 17.05 / 1.50 = 11.4 11.3666666666 C. Significant figures How about this one: (not in your notes; use calc) 1.2 0.34 0.601 0.5 20 D. SI base units Quantity Unit Abb. Length Mass Meter m Kilogram kg Time Second s Temperature Kelvin K Amount of substance E. Current Mole Ampere mol Luminous intensity candela cd Scientific researchers use ONLY these units! A We won’t D. SI Base units cont. Derived units – Made up of the base units Quantity SI Unit Other Units Area m2 acres, cm2, ft2 Volume m3 L, gal, cm3 Density kg g m 3 Speed m Energy kg m2 cm3 slugs ft3 mi/hr, ft/s s s 2 Calorie, kWhr E. Unit Conversions – metric prefixes kilo hecto deca unit deci centi milli king hector Doesn't Usually Drink Chocolate milk u g,m,L, etc. EXAMPLES 1 000g = ________ Kg 0.043 dam = _______ mm 0.23 Kg =________ dg 15.25 cL = ________ HL 345 DaL = _____ Km 101.34 Km = ___________ mm F. Metric conversions – conversion factors All conversions start with an EQUALITY 1 inch is the same as 2.54 cm 1 inch = 2.54 cm Equalities are turned into conversion factors: 1inch 2.54cm or 2.54cm 1inch Notice the top and bottom are same length! F. Metric conversions – conversion factors Convert 34 inches to centimeters 34 in 2.54 cm 1 in Conversion factor goes here 86.36 cm F. Metric conversions – conversion factors The Bulldogs need 550 cm for a first down. How MULTImany yards is that? STEP Plan: cm inch feet yards yd in 1 ft 1 1 550 cm 6 yards 2.54 cm 12 in 3 ft F. Metric conversions – conversion factors A baseball is thrown 60 ft/s. How fast is this in Two things miles/hour? to convert. Do one at 1. ft miles a time. 2. s min hours ft 1 mi 60 s 5280 ft 60 s 60 min 40.91 mi/hr 1 hr 1 min F. Metric conversions – powered units Misconception: 1 m = 100 cm but 1m3 ≠ 100 cm3 1 m3 cube 1m 100 cm 1m 100 cm 1m 100 cm So, 100x100x100 = 1,000,000 cm3 If the unit is cubed, you cube the numbers too (1 m)3 = (100 cm)3 1 m3 = 1,000,000 cm3 F. Metric conversions – Volumes Critical equality: 1 ml = 1 cm3 How many liters of fuel does a 300 m3 tank hold? 3 cm 1,000,000 3 300 m 3 1 m 1 ml 1 L 300,000 L 3 1 cm 1,000 ml Or you could do King Hector F. Metric conversions - Temperature 180 Fo = ? K Thou shalt use: Work: F C 32 o F 32 o C 9 o 9 5 o 5 C 82.2 o K C 273 o o F C 32 o 9 5 K C o 273 K 355K o G. Density Measure of how tightly packed matter is. More dense Floating Boat on SF6 Inhaling SF6 G. Density, cont. mass m D volume V g g or Units: 3 cm ml When measuring LxWxH When measuring Volume w/ cylinder G. Density, cont. A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? Given: D = 0.87 g/mL V=? M = 25 g m D V Work: m V D 25g V .87 g/ml V 28.74ml V 29ml(sigfigs) H. Percent Error Va Ve %E Va %E = Percent error Va = Accepted value Ve = Experimental value Example: A student measures the density of a solid as 3.42 g/cc. The solid really has a density of 3.76 g/cc. Calculate the percent error. cc = cubic centimeter Va = 3.76 g/cc Ve = 3.42 g/cc H. Percent Error, cont Given: Work: Va = 3.76 g/cc Ve = 3.42 g/cc Va Ve %E Va Watch parentheses here!!! 3.76 3.42 %E 3.76 %E = 0.09042 %E = 9.04% (sig figs) You can ignore negative signs. A positive percent means the accepted value is higher than your value. A negative means it’s lower.