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Measurement and Units Chapter 2
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SI System SI System = metric system Used world-wide Based on powers of 10 (everything is a factor of 10) Easy to convert units
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SI Base units Temperature - Kelvin (K) Time - second (s) Mass - gram (g) Length - meter (m) *Volume - Liter (L) (*derived unit) These base units can have prefixes attached to them to give them new meaning
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Metric Prefixes- pg. 33 PrefixPrefix Symbol Multiplier mega-M10 6 = 1 000 000 kilo-k10 3 = 1 000 BASE UNIT -gram -meter -Liter -second -10 0 = 1 centi-c10 -2 = 0.01 milli-m10 -3 = 0.001 micro-μ10 -6 = 0.000 001
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Powers of 10 A bigger power of 10… Ex: 10 9 > 10 3 Ex: 10 -1 > 10 -4 …means that there are MORE of the smaller unit Ex: 10 3 > 10 0 = 1000 meters in 1 kilometer (kilo-) (-meter) Ex: 10 0 > 10 -3 = 1000 milligrams in 1 gram (-gram) (milli-)
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Is 5.0 different than 5.00?
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Uncertainty in Measurement Measuring tools have limits. Only the last reported digit is estimated-- everything else is known for certain Need to figure out what each marking on the tool means so you know where to stop reporting digits Accuracy vs. precision Accuracy: How close you are to the accepted value Precision: How close all of your measurements are to each other
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Significant Figures Significant Figures (sig. figs.): the number of digits that carry meaning contributing to the precision of a measurement or calculated data. Include all known digits + one estimated digit 5.0 cm IS different from 5.00 cm, because you are able to measure out to different places. Affects measurements, rounding, and calculations
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Sig Fig rules All NON-ZERO digits (1-9) are ALWAYS significant Exact numbers (where there is no uncertainty) have an INFINITE number of sig figs 36 inches = 1 yard 100 cm = 1 m There are 12 oranges
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Sig Fig Rules: 0’s 0’s in the MIDDLE of non-zero digits are ALWAYS significant 501.1 cm = 4 sig figs 501.10 cm = 5 sig figs 0’s at the BEGINNING of a non-zero digit are NEVER significant 0.000849 kg = 3 sig figs 0.0008490 kg = 4 sig figs 0’s at the END of a number are ONLY significant IF there is a decimal 849,000 = 3 sig figs 849,000. = 6 sig figs
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Sig. Figs. Practice 1) 0.020110 L 2)730800 kg 3) 48381 m 4) 9807000 mm 5) 0.008401 mL 6) 40.500 s 7) 64000 km 8) 64000.00 km
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Rounding Sig. Figs. After you determine the amount of sig figs that a number should have…(based on the type of calculation…more to come) Round to that number of digits without changing the value of the number too much. Ex. 1) 7.867 g to 2 sig figs Ex. 2) 89.33 cm to 3 sig figs Ex. 3) 89,370. km to 3 sig figs Ex. 4) 0.0084386 s to 3 sig figs
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Calculations w/Sig Figs Add/Subtract: Round to the least precise digit. Keep the fewest number of decimal places Include units Example: 28.0 cm + 23.538 cm + 25.68 cm = 77.218 cm 28.0 cm was the least precise measurement, so round to 77.2 cm
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Example 4.32 cm – 1 cm Answer: 3 cm
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Calculations w/Sig Figs Multiply/Divide Round to the least precise measurement Least number of sig figs total Include units Example: 4,980,000 km x 0.0028 km = 13,944 km 2 …Answer can only have 2 sig figs, so round to 14,000 km 2
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Example 364.530 mm / 0.204 s Answer: 1790 mm/s
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Review rules for calculating Adding/subtracting: least number of decimal places Multiplying/dividing: least number of sig figs
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Dimensional Analysis: Converting units—2 measurements are equal to each other, but the units are different Units need to cancel Show your work, round for sig figs at the end
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Density A physical property of matter Can be used to identify unknown elements The amount of mass per unit volume For solids: g/cm 3 For liquids & gases: g/mL D = M V
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If a solid piece of metal has a mass of 13.5 g, and the volume is 5.0 cm 3, calculate the density of the metal. If an unknown liquid has a density of 0.998 g/mL, and the mass of the sample is 2.014 g, calculate the volume of the sample.
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