5 B. Percent Error Indicates accuracy of a measurement your value given value
6 B. 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 %
7 C. 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
8 C. Significant FiguresSame object with different rulers:
9 C. Significant Figures 739 5085 2.60 Counting Sig Figs Digits from 1-9 are always significant.Zeros 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
10 Counting Sig Fig Examples C. Significant FiguresCounting Sig Fig Examples4 sig figs3 sig figs3. 5,2803. 5,2803 sig figs2 sig figs
11 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
12 C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL Calculating with Sig Figs (cont’d)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 mL224 g+ 130 g354 g224 g+ 130 g354 g 7.9 mL 350 g
13 C. Significant Figures Calculating with Sig Figs (cont’d) Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm“1” in any conversion: 1 in = 2.54 cm
14 C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) 4 SF2 SF= g/mL 2.4 g/mL2 SFgg 18.1 g18.06 g
15 D. 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 diamond460,000,000,000,000,000,000,0004.6 x 1023Mass of one carbon atomg2 x gcoefficientexponent
16 D. 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 = exponent.Large # (>1) positive exponent Small # (<1) negative exponentOnly include sig figs – all of them!
17 D. Scientific Notation Practice Problems 7. 2,400,000 g 8. 0.00256 kg 10-5 km 104 mm2.4 106 g2.56 10-3 kgkm62,000 mm
18 D. Scientific Notation Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) =Type on your calculator:EXPEEEXPEEENTEREXE5.4478.1÷4== 670 g/mol= 6.7 × 102 g/mol
19 D. 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
20 HomeworkComplete Worksheet “Using Measurements – Chapter 2”: due tomorrow!
28 C. Density V = 825 cm3 M = DV D = 13.6 g/cm3 M = (13.6 g/cm3)(825cm3) An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.GIVEN:V = 825 cm3D = 13.6 g/cm3M = ?WORK:M = DVM = (13.6 g/cm3)(825cm3)M = 11,200 g
29 C. Density D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL 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/mLV = ?M = 25 gWORK:V = MDV = g0.87 g/mLV = 29 mL
31 A. Vocabulary 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
32 B. Dimensional Analysis The “Factor-Label” MethodUnits, or “labels” are canceled, or “factored” out
33 B. 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.
34 C. 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.
35 C. Conversion Factors 1. Liters and mL 2. Hours and minutes Learning Check: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
36 How many minutes are in 2.5 hours? Conversion factorcancel2.5 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!
37 D. Dimensional Analysis Practice You have $7.25 in your pocket in quarters. How many quarters do you have?4 quarters7.25 dollarsX= 29 quarters1 dollar
38 E. Dimensional Analysis Practice How many seconds are in 1.4days?Plan: days hr min seconds1.4 days x 24 hr x 60 min x 60 sec =day 1 hr minsecsec1.2 x105 sec
39 D. Dimensional Analysis Practice How many milliliters are in 1.00 quart of milk?qtmL1.00 qt1 L1.057 qt1000 mL1 L= 946 mL
40 D. Dimensional Analysis Practice 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
41 D. Dimensional Analysis Practice 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= 3.1 in
42 D. Dimensional Analysis Practice 6) Roswell 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
43 D. Dimensional Analysis Practice 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?mpieces1.3 m100 cm1 m1 piece1.5 cm= 86 pieces
44 D. Dimensional Analysis Practice 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