2 Measurement What is measurement? Quantitative ObservationBased on a comparison to an accepted scale.A measurement has 2 Parts – the Number and the UnitNumber Tells ComparisonUnit Tells ScaleThere are two common unit scalesEnglishMetric2
4 The measurement System units English (US)Length – inches/feetDistance – mileVolume – gallon/quartMass- poundMetric (rest of the world)Length – meterDistance – kilometerVolume – literMass - gram
5 Related Units in the Metric System All units in the metric system are related to the fundamental unit by a power of 10The power of 10 is indicated by a prefixThe prefixes are always the same, regardless of the fundamental unit6
7 Fundamental SI UnitsPhysical QuantityName of UnitAbbreviationMassKilogramkgLengthMetermTimeSecondsTemperatureKelvinKEnergyJoulesJPressurePascalPaVolumeCubic metersm3Established in 1960 by an international agreement to standardize science unitsThese units are in the metric system
8 Length….. SI unit = meter (m) About 3½ inches longer than a yard 1 meter = distance between marks on standard metal rod in a Paris vault or distance covered by a certain number of wavelengths of a special color of lightCommonly use centimeters (cm)1 inch (English Units) = 2.54 cm (exactly)7
9 Figure 2.1: Comparison of English and metric units for length on a ruler.
10 VolumeMeasure of the amount of three-dimensional space occupied by a substanceSI unit = cubic meter (m3)Commonly measure solid volume in cubic centimeters (cm3)Commonly measure liquid or gas volumein milliliters (mL)1 L is slightly larger than 1 quart1 mL = 1 cm38
11 Mass Measure of the amount of matter present in an object SI unit = kilogram (kg)Commonly measure mass in grams (g) or milligrams (mg)1 kg = pounds, 1 lbs.. = g9
12 Temperature ScalesAny idea what the three most common temperature scales are?Fahrenheit Scale, °FWater’s freezing point = 32°F, boiling point = 212°FCelsius Scale, °CTemperature unit larger than the FahrenheitWater’s freezing point = 0°C, boiling point = 100°CKelvin Scale, K (SI unit)Temperature unit same size as CelsiusWater’s freezing point = 273 K, boiling point = 373 K22
13 Thermometers based on the three temperature scales in (a) ice water and (b) boiling water.
15 Scientific NotationTechnique Used to Express Very Large or Very Small Numbers135,000,000,000,000,000,000 meterslitersBased on Powers of 10What is power of 10 Big?0,10, 100, 1000, 10,000100, 101, 102, 103, 104What is the power of 10 Small?0.1, 0.01, 0.001,10-1, 10-2, 10-3, 10-43
16 Writing Numbers in Scientific Notation 1. Locate the Decimal Point : 1, Move the decimal point to the right of the non-zero digit in the largest place - The new number is now between 1 and Now, multiply this number by a power of 10 (10n), where n is the number of places you moved the decimal point - In our case, we moved 3 spaces, so n = 3 (103)4
17 The final step for the number…… 4. Determine the sign on the exponent nIf the decimal point was moved left, n is +If the decimal point was moved right, n is –If the decimal point was not moved, n is 0We moved left, so 3 is positive1.438 x 1035
18 Writing Numbers in Standard Form We reverse the process and go from a number in scientific notation to standard form…..Determine the sign of n of 10nIf n is + the decimal point will move to the rightIf n is – the decimal point will move to the leftDetermine the value of the exponent of 10Tells the number of places to move the decimal pointMove the decimal point and rewrite the numberTry it for these numbers: x 106 and 9.8 x 10-2
19 Let’s Practice….. Change these numbers to Scientific Notation: 1,340,000,000,000697, 000Change these numbers to Standard Form:3.76 x 10-58.2 x 1081.0 x 1011.34 x 10126.97 x 1059.12 x 10-12820,000,00010
21 Uncertainty in Measured Numbers cmA measurement always has some amount of uncertainty, you always seem to be guessing what the smallest division is…To indicate the uncertainty of a single measurement scientists use a system called significant figuresThe last digit written in a measurement is the number that is considered to be uncertain10
22 Rules, Rules, Rules….We follow guidelines (i.e. rules) to determine what numbers are significantNonzero integers are always significant275389.659.281ZerosCaptive zeros are always significant (zero sandwich)1001.4
23 Significant Figures – Tricky Zeros Leading zeros never count as significant figuresTrailing zeros are significant if the number has a decimal point22,00063,850.100,000
24 Significant Figures Scientific Notation All numbers before the “x” are significant. Don’t worry about any other rules.7.0 x 10-4 g has 2 significant figures2.010 x 108 m has 4 significant figuresHow many significant figures are in these numbers?102, ,0171.0 x ,1,908, x 1014
26 Exact Numbers Exact Numbers are numbers known with certainty Unlimited number of significant figuresThey are eithercounting numbersnumber of sides on a squareor defined100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm1 kg = 1000 g, 1 LB = 16 oz1000 mL = 1 L; 1 gal = 4 qts.1 minute = 60 seconds14
27 Calculations with Significant Figures Exact numbers do not affect the number of significant figures in an answerAnswers to calculations must be rounded to the proper number of significant figuresround at the end of the calculationFor addition and subtraction, the last digit to the right is the uncertain digit.Use the least number of decimal placesFor multiplication, count the number of sig figs in each number in the calculation, then go with the smallest number of sig figsUse the least number of significant figures15
28 Rules for Rounding Off If the digit to be removed is less than 5, the preceding digit stays the sameRound to 4 sig figs.is equal to or greater than 5, the preceding digit is increased by 1Round to 3 sig figs.In a series of calculations, carry the extra digits to the final result and then round offDon’t forget to add place-holding zeros if necessary to keep value the same!! Round 80,150,000 to 3 sig figs.
29 Examples of Sig Figs in Math Answers must be in the proper number of significant digits!!!5.18 x116.8 – 0.33
30 Solutions: 0.107744 round to proper # sig fig 165.47 116.47 5.18 has 3 sig figs, has 3 sig figs so answer is 0.108165.47Limiting number of sig figs in addition is the smallest number of decimal places = 12 (no decimals) answer is 165116.47Same rule as above so answer is 116.5
32 Exact Numbers Exact Numbers are numbers known with certainty They are eithercounting numbersnumber of sides on a squareor defined100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm1 kg = 1000 g, 1 LB = 16 oz1000 mL = 1 L; 1 gal = 4 qts.1 minute = 60 seconds14
34 Movement in the Metric system In the metric system, it is easy it is to convert numbers to different units.Let’s convert 113 cm to metersFigure out what you have to begin with and where you need to go..How many cm in 1 meter?100 cm in 1 meterSet up the math sentence, and check that the units cancel properly.113 cm [1 m/100 cm] = m
35 Let’s Practice converting metric units 250 mL to Liters0.250 mL1.75 kg to grams1,750 grams88 µL to mL0.088 mL475 cg to kg47,500,000 or4.75 x 107328 mm to dm3.28 dmnL to µL0.75 µL
36 Converting Between Metric and non-Metric (English) units
37 Converting non-Metric Units Many problems involve using equivalence statements to convert one unit of measurement to anotherConversion factors are relationships between two unitsConversion factors are generated from equivalence statementse.g. 1 inch = 2.54 cm can give or18
38 Converting non-Metric Units Arrange conversion factor so starting unit is on the bottom of the conversion factorConvert kilometers to milesYou may string conversion factors together for problems that involve more than one conversion factor.Convert kilometers to inchesFind the relationship(s) between the starting and final units.Write an equivalence statement and a conversion factor for each relationship.Arrange the conversion factor(s) to cancel starting unit and result in goal unit.19
39 Practice Convert 1.89 km to miles Convert 5.6 lbs to grams Find equivalence statement 1mile = km1.89 km (1 mile/1.609 km)1.17 milesConvert 5.6 lbs to gramsFind equivalence statement 454 grams = 1 lb5.6 lbs(454 grams/1 lb)2500 gramsConvert 2.3 L to pintsFind equivalence statements: 1L = 1.06 qts, 1 qt = 2 pints2.3 L(1.06 qts/1L)(2 pints/1 qt)4.9 pints
40 Temperature Conversions To find Celsius from FahrenheitoC = (oF -32)/1.8To find Fahrenheit from CelsiusoF = 1.8(oC) +32Celsius to KelvinK = oC + 273Kelvin to CelsiusoC = K – 273
41 Temperature Conversion Examples 180°C to KelvinTo convert Celsius to Kelvin add 273= 453 K23°C to FahrenheitUse the conversion factor: F = (1.80)C + 32F = (1.80)F=73.4 or 73°F87°F to CelsiusUse the conversion factor C=5/9(F-32)C = 5/9(87-32)C = … or 31°C694 K to CelsiusTo convert K to C, subtract 273= 421°C
43 DensityDensity is a physical property of matter representing the mass per unit volumeFor equal volumes, denser object has larger massFor equal masses, denser object has small volumeSolids = g/cm3Liquids = g/mLGases = g/LVolume of a solid can be determined by water displacementDensity : solids > liquids >>> gasesIn a heterogeneous mixture, denser object sinks23
46 Density Example Problems What is the density of a metal with a mass of g whose volume occupies 6.30 cm3?What volume of ethanol (density = g/mL) has a mass of 2.04 lbs?What is the mass (in mg) of a gas that has a density of g/L in a 500. mL container?
48 Volume by displacement To determine the volume to insert into the density equation, you must find out the difference between the initial volume and the final volume.A student attempting to find the density of copper records a mass of 75.2 g. When the copper is inserted into a graduated cylinder, the volume of the cylinder increases from 50.0 mL to mL. What is the density of the copper in g/mL?
49 A student masses a piece of unusually shaped metal and determines the mass to be grams. After placing the metal in a graduated cylinder, the water level rose from 50.0 mL to 60.2 mL. What is the density of the metal?A piece of lead (density = g/cm3) has a mass of g. If a student places the piece of lead in a graduated cylinder, what is the final volume of the graduated cylinder if the initial volume is 10.0 mL?
50 Percent ErrorPercent error – absolute value of the error divided by the accepted value, multiplied by 100%.% error = measured value – accepted value x 100%accepted valueAccepted value – correct value based on reliable sources.Experimental (measured) value – value physically measured in the lab.
51 Percent Error ExampleIn the lab, you determined the density of ethanol to be g/mL. The accepted density of ethanol is g/mL. What is the percent error?The accepted value for the density of lead is g/cm3. When you experimentally determined the density of a sample of lead, you found that a 85.2 gram sample of lead displaced 7.35 mL of water. What is the percent error in this experiment?
52 Joe measured the boiling point of hexane to be 66. 9 °C Joe measured the boiling point of hexane to be 66.9 °C. If the actual boiling point of hexane is 69 °C , what is the percent error?A student calculated the volume of a cube to be cm3. If the true volume is cm3, what is the student’s percent error?Tom used the density of copper and the volume of water displaced to measure the mass of a copper pipe to be g. When he actually weighed the sample, he found a mass of g. What was his percent error?