Measurement and Units Chapter 2

SI System  SI System = metric system Used world-wide Based on powers of 10 (everything is a factor of 10) Easy to convert units

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

Metric Prefixes- pg. 33 PrefixPrefix Symbol Multiplier mega-M10 6 = kilo-k10 3 = BASE UNIT -gram -meter -Liter -second = 1 centi-c10 -2 = 0.01 milli-m10 -3 = micro-μ10 -6 =

Powers of 10 A bigger power of 10… Ex: 10 9 > 10 3 Ex: > …means that there are MORE of the smaller unit Ex: 10 3 > 10 0 = 1000 meters in 1 kilometer (kilo-) (-meter) Ex: 10 0 > = 1000 milligrams in 1 gram (-gram) (milli-)

 Is 5.0 different than 5.00?

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

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

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

Sig Fig Rules: 0’s  0’s in the MIDDLE of non-zero digits are ALWAYS significant cm = 4 sig figs cm = 5 sig figs  0’s at the BEGINNING of a non-zero digit are NEVER significant kg = 3 sig figs 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

Sig. Figs. Practice 1) L 2) kg 3) m 4) mm 5) mL 6) s 7) km 8) km

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) g to 2 sig figs  Ex. 2) cm to 3 sig figs  Ex. 3) 89,370. km to 3 sig figs  Ex. 4) s to 3 sig figs

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 cm cm = cm 28.0 cm was the least precise measurement, so round to 77.2 cm

Example  4.32 cm – 1 cm  Answer: 3 cm

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 km = 13,944 km 2 …Answer can only have 2 sig figs, so round to 14,000 km 2

Example  mm / s  Answer: 1790 mm/s

Review rules for calculating  Adding/subtracting: least number of decimal places  Multiplying/dividing: least number of sig figs

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

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

 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 g/mL, and the mass of the sample is g, calculate the volume of the sample.