9English vs. Metric Units Which is longer?A. 1 mile or 1 kilometerB. 1 yard or 1 meterC. 1 inch or 1 centimeter1.6 kilometers1 mile1 yard = meters1 inch = 2.54 centimetersLeft Image: Right Image:
10Metric UnitskmmcmmmThe basic unit of length in the metric system in the meter and is represented by a lowercase m.Metric Units1 Kilometer (km) = 1000 meters 1 Hectometer (hm) = 100 meters1 Meter = 100 Centimeters (cm) 1 Dekameter (dam) =10 meters1 Meter = 1000 Millimeters (mm) 1 Meter = 10 Decimeters (dm)Which is larger?A. 1 meter or 105 centimetersB. 4 kilometers or 4400 metersC. 12 centimeters or 102 millimetersD millimeters or 1 meter
11Measuring Length How many millimeters are in 1 centimeter? 1 centimeter = 10 millimetersHow many millimeters are in 1 centimeter?What is the length of the line in centimeters? _______cmWhat is the length of the line in millimeters? _______mmWhat is the length of the line to the nearest centimeter? ________cmHINT: Round to the nearest centimeter – no decimals.Ruler:
13English vs. Metric Units 1 pound = gramsWhich is larger?1. 1 Pound or 100 Grams2. 1 Kilogram or 1 Pound3. 1 Ounce or 1000 Milligrams100 kg = pounds1 ounce of gold = 28,349.5 milligrams
14Kilogram Prototype Image - http://en.wikipedia.org/wiki/Kilogram Metric UnitskggcgmgMass refers to the amount of matter in an object.The base unit of mass in the metric system is the kilogram and is represented by kg.Metric Units1 Kilogram (kg) = 1000 Grams (g) 1 Hectogram (hg) = 100 grams1 Gram (g) = 1000 Milligrams (mg) 1 Dekagram (dag) =10 grams1 Gram (g) = 100 Centigrams (cg) 1 Gram = 10 Decigrams (dg)Which is larger?A. 1 kilogram or 1500 gramsB milligrams or 1 gramC. 12 milligrams or 12 kilogramsD. 4 kilograms or 4500 gramsKilogram Prototype Image -
15_______ + ______ + _______ = ________ g Measuring MassWe will be using triple-beam balances to find the mass of various objects.The objects are placed on the scale and then you move the weights on the beams until you get the lines on the right-side of the scale to match up.Once you have balanced the scale, you add up the amounts on each beam to find the total mass.What would be the mass of the object measured in the picture?_______ + ______ + _______ = ________ gTop Image: Bottom Image:
17English vs. Metric Units Which is larger?A. 1 liter or 1 gallonB. 1 liter or 1 quartC. 1 milliliter or 1 fluid ounce1 fl oz = ml1 12-oz can of soda would equal approximately 355 ml.1 gallon = 3.79 litersIt would take approximately 3 ¾ 1-liter bottles to equal a gallon.1 quart = liters
18Liter Image: http://www.dmturner.org/Teacher/Pictures/liter.gif Metric UnitskLcLmLLVolume is the amount of space an object takes up.The base unit of volume in the metric system is the liter and is represented by L.Metric Units1 liter (L) = 1000 milliliters (mL)1 milliliter (mL) = 1 cm31 Kiloliter (kL) = 1000 Liters (L) 1 Hectoliters (hL) = 100 Liters1 Dekaliter (daL) =10 Liters 1 Liter (L) = 100 Centiliters (cL) Liter (L) = 10 Deciliters (dL)Which is larger?A. 1 liter or 1500 millilitersB. 200 milliliters or 1.2 litersC. 12 cm3 or 1.2 millilitersLiter Image:
19Measuring VolumeWe will be using graduated cylinders to find the volume of liquids and other objects.Read the measurement based on the bottom of the meniscus or curve. When using a real cylinder, make sure you are eye-level with the level of the water.What is the volume of water in the cylinder? _____mLWhat causes the meniscus?A concave meniscus occurs when the molecules of the liquid attract those of the container. The glass attracts the water on the sides.Top Image: Bottom Image:
20Measuring Liquid Volume What is the volume of water in each cylinder?Images created atABCPay attention to the scales for each cylinder.
21Measuring Solid Volume 10 cm9 cm8 cmWe can measure the volume of regular object using the formula length x width x height._____ X _____ X _____ = _____We can measure the volume of irregular object using water displacement.Amount of H2O with object = ______ About of H2O without object = ______ Difference = Volume = ______Click here for an online activity about volume. Choose Lessons Volume & Displacement
22Converting UnitsConversion Factor – equal ratio that enables you to change one unit to anotherExample:1kg = 1000 g1kg g1000g or kg22
35Density PracticeWhat is the density of a block of marble that occupies 310cm3 and has a mass of 853 grams?
36Density PracticeA diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.35 cm3?
37Density PracticeWhat is the volume of a sample of liquid mercury that has a mass of 76.2g, given that the density of mercury is 13.6 g/ml ?
38Now… Density Worksheet 1 & 2 Homework: Quiz over p. 42 (1-5) – next class
39Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty39
40Why Is there Uncertainty? Measurements are performed with instrumentsNo instrument can read to an infinite number of decimal places
41Which of these balances has the greatest uncertainty in measurement?
42Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT Accuracy - how close a measurement is to the accepted valuePrecision - how close a series of measurements are to each otherACCURATE = CORRECTPRECISE = CONSISTENT
46Experimental Data Carbon = 12.0107 amu During your experiment, you obtained the following values: , ,Are these Precise or Accurate?
47Percent Error Indicates accuracy of a measurement % error = Accepted – Experimental x Accepted
48Percent Error % error = - 2.9 % 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 = 1.36 – x 100=% error = %
49Significant Figures Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit2.35 cm
50Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.3456 has4 sig figs.
51Rules for Counting Significant Figures - Details Zeros-Beginning zeros do not count as significant figures.has3 sig figs
52Rules for Counting Significant Figures - Details Zeros- Middle zeros always count as significant figures.16.07 has4 sig figs.
53Rules for Counting Significant Figures - Details ZerosEnd zeros are significant only if the number contains a decimal point.9.300 has4 sig figs.
54Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.1 inch = cm, exactly
55Counting Sig Fig Examples Significant FiguresCounting Sig Fig Examples____ sig figs___ sig figs3. 5,2803. 5,280____ sig figs____ sig figs
56Sig Fig Practice #1How many significant figures in each of the following?m 5 sig figs17.10 kg 4 sig figsL 3.29 x 103 s 3 sig figscm 2 sig figs
57Significant 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
58Rules for Significant Figures in Mathematical Operations 6.38 x 2.0 =12.76 13 (2 sig figs)
59Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m ____ m __ m2100.0g ÷ 23.7cm3 ________ g/cm3 ____g/cm30.02cm x 2.371cm ______ cm ____ cm2710 m ÷ 3.0 s ________ m/s ____ m/s
60Significant 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 mL 7.9 mL
61Significant 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
62Significant Figures Practice Problems 6. 18.9 g - 0.84 g 18.06 g 5. (15.30 g) ÷ (6.4 mL)4 SF2 SF= g/mL 2.4 g/mL2 SFgg 18.1 g18.06 g
63Scientific Notation In science, we deal with some very LARGE numbers: 1 mole =In science, we deal with some very SMALL numbers:Mass of an electron =kg
64Imagine the difficulty of calculating the mass of 1 mole of electrons! kgx??????????????????????????????????
65Scientific Notation:A method of representing very large or very small numbers in the form:M x 10nM is a number between 1 and 9.9n is an integer
66. 2 500 000 000 Step #4: Re-write in the form M x 10n 9 8 7 6 5 4 3 2 Step #1: Insert an understood decimal pointStep #2: Decide where the decimal must endup so that one number is to its leftStep #3: Count how many places you bouncethe decimal pointStep #4: Re-write in the form M x 10n
672.5 x 109The exponent is the number of places we moved the decimal.
680.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bouncethe decimal pointStep #4: Re-write in the form M x 10n
695.79 x 10-5The exponent is negative because the number we started with was less than 1.
71Scientific Notation Practice Problems ________g 7. 2,400,000 g kg9. 7 10-5 km 104 mm________ kg________ km_______ mm
72Scientific Notation Type on your calculator: = 671.6049383 = 670 g/mol 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
73Direct Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increaseAs the value of one variable decreases, the other must also decreaseThe graph of a direct proportion is a straight line
74Inverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decreaseAs the value of one variable decreases, the other must increaseThe graph of an inverse proportion is a hyperbola