5B. Percent Error your value given value Indicates accuracy of a measurementyour valuegiven value
6B. Percent Error % error = 2.94 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.% error = 2.94 %
7C. Significant Figures Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit2.31 cm
8C. Significant Figures 739 5085 2.60 Counting Sig Figs Digits from 1-9 are always significantZeros between two other sig figs are always significantOne or more additional zeros to the right of both the decimal place and another sig digit are significantCount all numbers EXCEPT:Leading zerosTrailing zeros without a decimal point -- 2,50073950852.60
9Counting Sig Fig Examples C. Significant FiguresCounting Sig Fig Examples4 sig figs3 sig figs3. 5,2803. 5,2803 sig figs2 sig figs
10C. 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
11C. 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 answer3.75 mLmL7.85 mL3.75 mLmL7.85 mL 7.9 mL
12C. Significant Figures Calculating with Sig Figs (con’t) Exact Numbers do not limit the # of sig figs in the answerCounting numbers: 12 studentsExact conversions: 1 m = 100 cm“1” in any conversion: 1 in = 2.54 cm
14D. Scientific NotationA way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent)Number of carbon atoms in the Hope diamond460,000,000,000,000,000,000,000 atoms4.6 x atomscoefficientexponent
15D. Scientific Notation 65,000 kg 6.5 × 104 kg Converting into Sci. Notation:Move decimal until there’s 1 digit to its left. Places moved = exponentLarge # (>1) positive exponent Small # (<1) negative exponentOnly include sig figs – all of them!
16D. Scientific Notation Practice Problems 7. 2,400,000 g kg 10-5 km 104 mm2.4 106 g2.56 10-3 kgkm62,000 mm
18D. Scientific Notation Practice Problems 4 1010 cm2 6.9 10-2 kg2 11. (4 x 102 cm) x (1 x 108cm)12. (2.1 x 10-4kg) x (3.3 x 102 kg)13. (6.25 x 102) ÷ (5.5 x 108)14. (8.15 x 104) ÷ (4.39 x 101)15. (6.02 x 1023) ÷ (1.201 x 101)6.9 10-2 kg21.1 x 10-61.86 x 1035.01 x 1022
24B. Dimensional Analysis A tool often used in science for converting units within a measurement systemConversion FactorA numerical factor by which a quantity expressed in one system of units may be converted to another system
25B. Dimensional Analysis The “Factor-Label” MethodUnits, or “labels” are canceled, or “factored” out
26B. Dimensional Analysis Steps to solving problems: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.
27C. Conversion Factors Example: 1 in. = 2.54 cm Fractions in which the numerator and denominator are EQUAL quantities expressed in different unitsExample: in. = 2.54 cmFactors: 1 in and cm2.54 cm in.
28How many minutes are in 2.5 hours? Conversion factor cancel2.5 hr1x60 min1 hr= 150 minBy using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!
29C. Conversion Factors 1. Liters and mL 2. Hours and minutes Write conversion factors that relate each of the following pairs of units:1. Liters and mL2. Hours and minutes3. Meters and kilometers1 L1000 mL1000 mL1 L=1 hr60 min1000 m1 km
30D. SI Prefix Conversions 1. Memorize the following chart. (next slide)Find the conversion factor(s).Insert the conversion factor(s) to get to the correct units.When converting to or from a base unit, there will only be one step. To convert to or from any other units, there will be two steps.
31A. SI Prefix Conversions SymbolFactortera-T1012giga-G109mega-M106kilo-k103hecto-h102deka-da101move leftmove rightBASE UNIT---100deci-d10-1centi-c10-2milli-m10-3micro-10-6nano-n10-9
32A. SI Prefix Conversions =532 m = _______ km0.532NUMBERUNITNUMBERUNIT