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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

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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/cm 3. Bob calculates the density three times and gets 2.75, 2.79 and 2.77. AVG: 2.77 Mary calculates the density three times and gets 4.66, 4.67, and 4.65 AVG: 4.66 Holden calculates the density three times and gets 10.25, 6.87, and 1.25 AVG: 6.12 Franz calculates the density three times and gets 2.90, 1.95, 3.44 AVG: 2.76 ACCURATE AND PRECISE ACCURATE BUT NOT PRECISE PRECISE BUT NOT ACCURATE NIETHER ACCURATE NOR PRECISE

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B. Measurement ___________ Something with magnitude, size or amount. Measurement ________ - Compares what is measured to a defined size. Unit ________ - The international system of measure that uses only BASE metric units SI ________ - Standard system of measure using base 10. Metric

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B. Measurement ___________ - Measurements having numbers or size. Quantitative ___________ - Measurement having subjective descriptions Qualitative Examples: 20 ml of water The reaction bubbles Uma Thurman is blonde 17 g/ml Bulldogs are #1 QUANTITATIVE QUALITATIVE

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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

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C. Significant figures Consider the following: What’s the estimate? This ruler isn’t as accurate as the previous.

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C. Significant figures RULEEXAMPLENO. OF SIG FIGS All nonzero digits and zeros between those digits are significant 1 458 g 40.7 m 10 150.01 mm Leading zeros with decimal points are NOT significant; Ending zeros ARE significant with decimal 0.0005 kg 0.01008 m 1 701.10 L 0.00140500 m Ending zeros left of the decimal point may or may not be significant. Indication needed. 15 000 kg 15 000. kg 1.50E4 kg 1.500E4 kg 4 3 7 1 4 6 6 2 5 3 Scientific notation is always in sig fig form 4

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C. Significant figures ADDITION AND SUBTRACTION Answer has as many DECIMAL POINTS as the part with the LEAST decimals. 5.44 – 2.6106 =2.4 – 15.82 = 2.099 + 0.05681 =0.258 +.1 = 2.8294 2.83 -13.42 -13.4 2.15581 2.156 0.3580.4

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C. Significant figures MULTIPLICATION AND DIVISION 8.15 x 6 =0.250 / 0.87 = 1.2 x 1010 =17.05 / 1.50 = 48.9 0.2873563218 121211.3666666666 Answer can only contain as many SIG FIGS as the part with the LEAST sig figs 50 0.29 1200 11.4

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C. Significant figures How about this one: (not in your notes; use calc) 20

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D. SI base units Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of substance Mole mol E. Current Ampere A Luminous intensitycandela cd QuantityUnitAbb. Scientific researchers use ONLY these units! We won’t

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D. SI Base units cont. Derived units – Made up of the base units QuantitySI UnitOther Units Area Volume Density Speed Energy m2m2 m3m3 acres, cm 2, ft 2 L, gal, cm 3 mi/hr, ft/s Calorie, kWhr

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E. Unit Conversions – metric prefixes kilohectodecaunitdecicentimilli kinghectorDoesn'tUsuallyDrinkChocolatemilk EXAMPLES 1 000g = ________ Kg0.043 dam = _______ mm 0.23 Kg =________ dg15.25 cL = ________ HL 345 DaL = _____ Km101.34 Km = ___________ mm

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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: Notice the top and bottom are same length!

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F. Metric conversions – conversion factors Convert 34 inches to centimeters 34 in in cm 1 2.54 Conversion factor goes here 86.36 cm

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F. Metric conversions – conversion factors The Bulldogs need 550 cm for a first down. How many yards is that? 550 cm MULTI- STEP Plan: cm inch feet yards cm in 2.54 1 in ft1 12ft yd 1 3 6 yards

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F. Metric conversions – conversion factors A baseball is thrown 60 ft/s. How fast is this in miles/hour? Two things to convert. Do one at a time. ft mi1 5280 s min 1 60 min hr1 60 40.91 mi/hr 1. ft miles 2. s min hours

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F. Metric conversions – powered units Misconception: 1 m = 100 cm but 1m 3 ≠ 100 cm 3 1 m 3 cube 1 m 100 cm So, 100x100x100 = 1,000,000 cm 3 If the unit is cubed, you cube the numbers too (1 m) 3 = (100 cm) 3 1 m 3 = 1,000,000 cm 3

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F. Metric conversions – Volumes Critical equality: How many liters of fuel does a 300 m 3 tank hold? 300 m 3 m3m3 cm 3 1 1,000,000 cm 3 ml 1 1 L 1 1,000 300,000 L Or you could do King Hector 1 ml = 1 cm 3

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F. Metric conversions - Temperature Thou shalt use: 180 F o = ? K Work:

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G. Density Measure of how tightly packed matter is. More dense

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Floating Boat on SF 6

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Inhaling SF 6

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G. Density, cont. Units: When measuring LxWxH When measuring Volume w/ cylinder

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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 Work:

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H. Percent Error %E = Percent error V a = Accepted value V e = Experimental value 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 V a = 3.76 g/ccV e = 3.42 g/cc Example:

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H. Percent Error, cont Given:Work: V a = 3.76 g/cc V e = 3.42 g/cc Watch parentheses here!!! You can ignore negative signs. A positive percent means the accepted value is higher than your value. A negative means it’s lower. %E = 0.09042 %E = 9.04% (sig figs)

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