7 SI MEASUREMENTSI units are defined in terms of standards of measurement. They are either objects or consistent natural phenomena.International organizations monitor the defining process. In the US, the National Institute of Standards and Technology plays a major role in setting standards
8 DERIVED UNITS 1) Derived SI units: combinations of SI base units Examples:density = massvolume
9 DERIVED UNITS 2) volume: amount of space occupied by an object non-SI volume unit:liter, L 1 L = 1000 cm3SI volume unit: m3
10 DERIVED UNITS 3) density: mass per unit volume d = m/V Mass and volume change proportionately, meaning that the ratio of m to V is constant. Density is an intensive property.Density and temperature: at high T, most objects expand.
11 SCIENTIFIC NOTATIONScientific Notation: numbers written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number.km 6.5 x 104 kmmm 1.2 x 10-3 mm
12 Scientific Notation Rules To find M: Move the decimal point in the original # to the left or right so that only one nonzero digit remains to the left of the decimal pointTo find n: Count the # of places that you moved the decimal point(Moved left, n = + Moved right, n = - )
13 SCIENTIFIC NOTATIONAddition and Subtraction: Values must have same value exponent before you can do these operationsMultiplication: M factors are multiplied and exponents are addedDivision: M factors divided and exponent of denominator subtracted from exponent of numerator
14 Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out
15 Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel.3. Multiply all top numbers & divide by each bottom number.4. Check units & answer.
16 Dimensional Analysis 1 in = 2.54 cm = 1 2.54 cm 2.54 cm 1 in = 2.54 cm Lining up conversion factors:= 11 in = 2.54 cm2.54 cm cm1 =1 in = 2.54 cm1 in in
17 Dimensional Analysis 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL qt mL How many milliliters are in 1.00 quart of milk?qtmL1.00 qt1 L1.057 qt1000 mL1 L= 946 mL
18 Dimensional Analysis 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.lbcm31.5 lb1 kg2.2 lb1000 g1 kg1 cm319.3 g= 35 cm3
19 Dimensional Analysis 75.0 in3 (2.54 cm)3 (1 in)3 1 L 1000 cm3 = 1.23 L How many liters of water would fill a container that measures 75.0 in3?in3L75.0 in3(2.54 cm)3(1 in)31 L1000 cm3= 1.23 L
20 Dimensional Analysis 8.0 cm 1 in 2.54 cm = 3.2 in cm in 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?cmin8.0 cm1 in2.54 cm= 3.2 in
21 Dimensional Analysis 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.0 yd 6) Taft football needs 550 cm for a 1st down. How many yards is this?cmyd550 cm1 in2.54 cm1 ft12 in1 yd3 ft= 6.0 yd
22 Dimensional Analysis 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces cm 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?cmpieces1.3 m100 cm1 m1 piece1.5 cm= 86 pieces
23 A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted valuePrecision - how close a series of measurements are to each otherACCURATE = CORRECTPRECISE = CONSISTENT
25 B. Percent Error your value accepted value Indicates accuracy of a measurementyour valueaccepted value
26 % Error ProblemsTry the two practice problems on the outline.
27 Percent Error Examples What is the % error for a mass measurement of 17.7 g if the correct value is 21.2 g?17.7 g – 21.2 g x 100 =21.2 gb. A volume is measured experimentally to be 4.26 mL. What is the % error if the correct value is 4.15 mL?4.26 mL – 4.15 mL x 100 =4.15 mL
28 ERROR IN MEASUREMENTIn any measurement, some error or uncertainty existsMeasuring instruments themselves place limitations in precisionEstimate the final questionable digit.
29 D. Significant Figures Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit2.35 cm
30 SIGNIFICANT FIGURES Significant ≠ Certain Must memorize the rules for recognizing significant figures!
31 SIG. FIGS. RULES RULE EXAMPLE 1. No zeros, All sig. 852 m 97.25 mL 2. Zeros between nonzero digits = sig.40.7 L km3. Zeros at front of nonzero digits ≠ sig.mkg4. Zeros at end of # and to right of decimal = sig.85.00 gmm5. Decimal after zeros, sig. Zeros with no decimal ≠ sig2000 m2000. m
32 Atlantic-Pacific Check Pacific, Atlantic,Decimal is Decimal isPresent Absent
33 Significant figures practice Try the practice problems on the outline
34 Sig. Figs. Practice 804.05 g 0.0144030 km 1002 m 400 mL 30000. cm kg
35 ROUNDING RULES < 5 Stay the same 5, followed by nonzero Digit after last digit to be kept:Last digit should:Examples (3 sig. Figs)> 5Increase by 142.68 g 42.7 g< 5Stay the same17.32 m 17.3 m5, followed by nonzerocm 2.79 cm5, preceded by odd4.635 kg 4.64 kg5, preceded by even78.65 mL 78.6 mL
36 C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL Calculating with Sig Figs (con’t)Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.3.75 mLmL7.85 mL3.75 mLmL7.85 mL 7.8 mL
37 C. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g Calculating with Sig FigsMultiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.(13.91g/cm3)(23.3cm3) = g4 SF3 SF3 SF324 g
38 Sig. Figs./Rounding Practice Try the practice problems on the outline.
39 Practice Problems 1. What is the sum of 2.099 and 0.05681? 2. Calculate the quantity 87.3 cm – cm3. Polycarbonate has a density of 1.2 g/cm3. A photo frame is constructed from two 3.0 mm sheets. Each side measures 28 cm by 22 cm. What is the mass of the frame?
40 Conversion Factors Conversion factors are typically exact. Do not count when determining # of significant figures in answer.
41 E. ProportionsDirect ProportionyxInverse Proportionyx
42 Direct and Indirect Proportions Direct: 2 quantities are directly proportional if dividing one by the other gives a constant value; graph is a straight line, y/x = kIndirect: 2 quantities are indirectly proportional if their product is constant, graph curved, xy = k or y α 1/xGRAPHS