2 Do Now: Hand in the Measuring activity – front of the room!! Identify different quantities that can be measured and their units of measurement.
3 Essential QuestionsWhat are the SI base units for time, length, mass, amount of substance and temperature?How does adding a prefix change a unit?How are the derived units different for volume and density?
4 Vocabulary Base unit Derived unit Second Liter Meter Density Kilogram MassKelvinMeasurement
5 What is a measurement?Comparison between an unknown and a standard.
6 SI & Base units Systeme Internationale d’Unites (SI) – Base Units An internationally agreed upon system of measurements.Base UnitsDefined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.
7 Base units Time – second Distance – Meter Mass – kilogram Based on the frequency of radiation given off by a cesium-133 atomDistance – MeterDistance light travels in a vacuum in 1/299,792,458th of a second.Mass – kilogramActual mass of 1 kilogram (see picture)Temperature – KelvinZero Kelvin (absolute zero) refers to the point where there is virtually no particle motion or kinetic energy.Two other commonly used scales; Fahrenheit and Celsius.
8 SI prefixes SI Prefixes are multipliers that precede the base unit. You must know the three that are outlined.
9 Derived units Not all quantities can be measured with SI base units. Derived Units – a unit that is defined as a combination of base units.Speed – The SI unit for speed is m/s (measurement of distance divided by time)Volume – SI unit for volume is cm3.
10 volume 1 mL – volume of liquid that occupies a 1cm x 1cm x 1cm cube 1 mL = 1 cm3QUESTION – How many mL in a 1m x 1m x 1m (1m3) box?
11 DensityDensity – derived unit that describes the amount of mass per unit of volume.g/cm3g/mLKg/L𝐷𝑒𝑛𝑠𝑖𝑡𝑦= 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒𝐷= 𝑚 𝑉
12 Density Sample Problem When a piece of aluminum is placed in a 25-mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. What is the mass of the aluminum? (density of aluminum is 2.7 g/mL).GIVEN (variable, number, units)V = 3 mLD = 2.7 g/mLUNKNOWN (variable, question mark, units)m = ? gFORMULA (no need to rearrange formula)D= m VSUBSTITUTION (Substitute in numbers with units)𝟐.𝟕 𝒈 𝒎𝒍 = 𝒎 𝟑 𝒎𝑳SOLUTION (Variable, number, units)m = 8.1 g
13 Sample Problem #2Question 116 g of sunflower oil is used in a recipe. The density of the oil is g/mL. What is the volume of the sunflower oil in mL?m = 116 g V = ? mLD = g/mL𝐷= 𝑚 𝑉0.925 𝑔 𝑚𝐿 = 116 𝑔 𝑉V = 125 mL
14 Density- Practice Problem 1 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 = ? gWORK:
15 Density – Practice Problem 1 Solution 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 = ? gWORK:M = DVM = (13.6 g/cm3)(825cm3)M = 11,200 g
16 Density – Practice Problem 2 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 = ? mLM = 25 gWORK:
17 Density – practice Problem 2 SOlution 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 = ? mLM = 25 gWORK:V = MDV = g0.87 g/mLV = 29 mL
19 Essential questions & vocabulary Why use scientific notation to express numbers?How is dimensional analysis used for unit conversions?VOCABULARYScientific notationDimensional analysisConversion factor
20 5,450,000 5.45 x 106 Scientific notation Used to express any numbers as a number between 1 and 10 multiplied by 10 raised to a power.5,450,000 5.45 x 106ExponentCoefficient
21 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.65,000 kg 6.5 × 104 kg
22 Scientific notation Positive Power – number larger than 1 2.3 x 105 230,000Negative power – number smaller than 12.3 x 10-5
23 Scientific Notation – Practice Problems 1) 2,400,000 g 2) kg 3) 7 10-5 km 4) 6.2 104 mm
24 Scientific Notation – Practice Solutions Convert the following to proper scientific notation1) 2,400,000 g 2) kg 3) 7 10-5 km 4) 6.2 104 mm2.4 106 g2.56 10-3 kgkm62,000 mm
25 Scientific Notation – Addition & Subtraction In order to add or subtract numbers written in scientific notation, the exponents must be the same!!!
26 scientific notation: Multiplication Multiply the coefficientsUse properties of exponents to multiply the power of 10Simplify
27 Scientific Notation: Division Divide the coefficients.Use properties of exponents to multiply the power of 10Simplify
29 Dimensional AnalysisDimensional Analysis: systematic approach to problem solving that uses conversion factors to move, or convert from one unit to another.Conversion Factor: ratio of equivalent values having different units.
30 Dimensional analysis: practice 360 s to ms72 g to mg4800 g to kg2.45 x 102 ms to s5600 dm to m5 g/cm3 to kg/m3
32 Essential Questions & Vocabulary How do accuracy and precision compare?How can the accuracy of experimental data be described using error and percent error?What are the rules for significant figures and how can they be used to express uncertainty in measured and calculated values?VOCABULARYAccuracyPercent ErrorPrecisionSignificant FigureError
33 BAKING COOKIESWhat are some of the measurements required in making cookies?Cup, tablespoon, Teaspoon.
34 Baking CookiesWould a batch of cookies turn out ok if all ingredients would be measured in teaspoons?NO!!! = too much error would build up.It is important to select appropriate measurement instruments based on the amounts needed!!!!
35 ACCURATE = CORRECT PRECISE = CONSISTENT Accuracy vs. PrecisionAccuracy - how close a measurement is to the accepted valuePrecision - how close a series of measurements are to each otherACCURATE = CORRECTPRECISE = CONSISTENT
36 Percent Error your value accepted value Indicates accuracy of a measurementyour valueaccepted value
37 Percent Error - Example 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 = 2.90 %
38 Significant Figures Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit
39 Significant Figures 2.35 cm Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit2.35 cm
40 Significant Figures Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500
41 Counting Sig Fig Examples Significant FiguresCounting Sig Fig Examples3. 5,2803. 5,280
42 Counting Sig Fig Examples Significant FiguresCounting Sig Fig Examples4 sig figs3 sig figs3. 5,2803. 5,2803 sig figs2 sig figs
43 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
44 Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 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 mL224 g+ 130 g354 g224 g+ 130 g354 g 7.9 mL 350 g
45 Significant Figures Calculating with Sig Figs (con’t) 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
46 Significant figures: practice problems 5. (15.30 g) ÷ (6.4 mL)4 SF2 SF 2.4 g/mL2 SF= g/mLgg18.06 g 18.1 g
47 Practice QuestionDetermine the number of significant figures in the following: 8,200, 723.0, and 0.01.A. 4, 4, and 3B. 4, 3, and 3C. 2, 3, and 1D. 2, 4, and 1
48 Percent Error: Practice Question A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error?A %B %C. 10 %D. 20 %
50 Essential questions & Vocabulary Why are graphs created?How can graphs be interpreted?VOCABULARYGraphInterpolationExtrapolation
51 GraphingA graph is a visual display of data that makes trends easier to see than in a table.A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.
52 GRAPHING – bar graphsBar graphs are often used to show how a quantity varies across categories.
53 Graphing – dependent & independent variables On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.
54 Graphing – finding the slope If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.
55 Interpreting graphsInterpolation is reading and estimating values falling between points on the graph.Extrapolation is estimating values outside the points by extending the line.This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.