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Dimensional analysis and Units of Measurements
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Dimensional analysis Dimensional analysis uses conversion factors to convert from one unit to another. Also called Factor Label (and railroad tracks) You do this in your head all the time – How many quarters are in 4 dollars?
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Dimensional analysis practice 3 Big Mac = 7 salads 9 salads = 2 slices of pepperoni pizza 22 slices of pepperoni pizza = 27 Sonic cokes Ex. 1) What number of Big Macs equal 365.4 salads? Ex. 2) How many sonic cokes do you have to drink to equal 11 salads?
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Units of Measurement Meter m Liter L Celsius C
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Mass is the amount of matter, weight is a measure of the gravitational pull on matter
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SI Units PrefixSymbolScientific notationFactorExample MegaM1 x 10 6 1,000,000megagram (Mg) Kilok1 x 10 3 1,000kilometer (km) Hectoh1 x 10 2 100hectoliter (hL) Dekada or (D)1 x 10 1 10dekagram (Dg) BASE UNIT1 x 10 0 1meter Decid1 x 10 -1.1deciliter (dL) Centic1 x 10 -2.01centimeter (cm) Millim1 x 10 -3.001milligram (mg) Microu1 x 10 -6.000001microgram (ug) Nanon1 x 10 -9.000000001nanometer (nm) Picop1 x 10 -12.000000000001picogram (pg)
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Practice In each pair below, circle the larger MillimeterCentimeter picometerMicrometer kilogramHectogram decilitermillileter
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Practice In each pair below, circle the larger MillimeterCentimeter picometerMicrometer kilogramHectogram decilitermillileter
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Practice In each pair below, circle the larger MillimeterCentimeter picometerMicrometer kilogramHectogram decilitermillileter
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Practice In each pair below, circle the larger MillimeterCentimeter picometerMicrometer kilogramHectogram decilitermillileter
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Practice In each pair below, circle the larger MillimeterCentimeter picometerMicrometer kilogramHectogram decilitermillileter
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Basic SI Units QuantityBase unit Lengthmeter (m) Massgram (g) Timesecond (s) VolumeLiter (L) TemperatureKelvin (K) or Celsius (C) Amount of substancemole (mol) Heat & Energyjoule (J)
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Metric Conversions Practice Ex. 3) 2.435 g __________________cg Ex. 4) 23.8 mL = ________________kL Ex. 5) 23.5 cs = ________________ns
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Some Useful Conversions Length: 1 in = 2.54 cm 1 mi = 5280 ft Volume: 1 cm 3 = 1 mL 1 L = 1.06 qt Weight: 1 kg = 2.2 lb 16 oz = 1 lb 1 ton = 2000 lb
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Temperature 20°C = K Use both the Kelvin and Celsius scale, to convert Celsius + 273 = Kelvin Kelvin -273 = Celsius
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Temperature 20°C = 293 K Use both the Kelvin and Celsius scale, to convert Celsius + 273 = Kelvin Kelvin -273 = Celsius
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Temperature 20°C = 293 K 373 K = °C Use both the Kelvin and Celsius scale, to convert Celsius + 273 = Kelvin Kelvin -273 = Celsius
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Temperature 20°C = 293 K 373 K = 100 °C Use both the Kelvin and Celsius scale, to convert Celsius + 273 = Kelvin Kelvin -273 = Celsius
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Volume: measured in cubic centimeters (cm 3 ) or liters 1 liter (L) = 1 cubic decimeter (dm 3 ) = 1000 millileters (mL) 1 mL= 1 cm 3
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Volume can be measure by Length x x or the Water Displacement method
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Volume can be measure by Length x width x or the Water Displacement method
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Volume can be measure by Length x width x height or the Water Displacement method
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Volume can be measure by Length x width x height or the Water Displacement method Know the relationship between the following volume units… L = mL = cm 3 (or cc in medical lingo)
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Volume can be measure by Length x width x height or the Water Displacement method Know the relationship between the following volume units… 1 L = mL = cm 3 (or cc in medical lingo)
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Volume can be measure by Length x width x height or the Water Displacement method Know the relationship between the following volume units… 1 L = 1000 mL = cm 3 (or cc in medical lingo)
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Volume can be measure by Length x width x height or the Water Displacement method Know the relationship between the following volume units… 1 L = 1000 mL = 1000 cm 3 (or cc in medical lingo)
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Density Is the ratio of mass per unit of volume. How much matter is packed into a given amount of space Density = mass/volume D= m/v
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The Density of a substance stays regardless of the size of the sample. For example: if you cut a block of copper in half, you have decreased both the mass and volume, the ratio of the 2 stays the same. This is called an Intensive Physical Property.
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The Density of a substance stays constant regardless of the size of the sample. For example: if you cut a block of copper in half, you have decreased both the mass and volume, the ratio of the 2 stays the same. This is called an Intensive Physical Property.
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The appropriate units of density are: for solids for liquids
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The appropriate units of density are: g/cm 3 for solids for liquids
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The appropriate units of density are: g/cm 3 for solids g/mL for liquids
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Example problems: A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm 3. Calculate the Density of aluminum.
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Example problems: A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm 3. Calculate the Density of aluminum. 8.4 g/3.1 cm 3 =
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Example problems: A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm 3. Calculate the Density of aluminum. 8.4 g/3.1 cm 3 = 2.7 g/cm 3
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Example problems: Diamond has a density of 3.26 g/cm 3. What is the mass of a diamond that has a volume of 0.350 cm 3 ?
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Example problems: Diamond has a density of 3.26 g/cm 3. What is the mass of a diamond that has a volume of 0.350 cm 3 ? 3.26 g/cm 3 x 0.350 cm 3 =
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Example problems: Diamond has a density of 3.26 g/cm 3. What is the mass of a diamond that has a volume of 0.350 cm 3 ? 3.26 g/cm 3 x 0.350 cm 3 = 1.14 g
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Example problems: What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL?
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Example problems: What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL? 76.2 g = 13.6 g/mL
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Example problems: What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL? 76.2 g = 5.60 mL 13.6 g/mL
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Reliable Measurements refers to the closeness of the measure value is to the, or real, value. refers to how a series of measurements are to one another.
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Reliable Measurements Accuracy refers to the closeness of the measure value is to the, or real, value. refers to how a series of measurements are to one another.
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Reliable Measurements Accuracy refers to the closeness of the measure value is to the accepted, or real, value. refers to how a series of measurements are to one another.
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Reliable Measurements Accuracy refers to the closeness of the measure value is to the accepted, or real, value. Precision refers to how a series of measurements are to one another.
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Reliable Measurements Accuracy refers to the closeness of the measure value is to the accepted, or real, value. Precision refers to how close a series of measurements are to one another.
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is calculated by subtracting the value from the value.
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Error is calculated by subtracting the experimental value from the accepted value.
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The is the ratio of an error to an accepted value.
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The percent error is the ratio of an error to an accepted value.
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% error = error x 100 = accepted value – experimental value x 100 accepted value accepted value
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Example An experiment finds the density of lead to be 10.95 g/cm 3. The literature value for the density of lead is 13.34 g/cm 3.
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The error: accepted value – experimental value= 13.34 – 10.95 = An experiment finds the density of lead to be 10.95 g/cm 3. The literature value for the density of lead is 13.34 g/cm 3.
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The error: accepted value – experimental value= 13.34 – 10.95 = 2.39 An experiment finds the density of lead to be 10.95 g/cm 3. The literature value for the density of lead is 13.34 g/cm 3.
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The error: accepted value – experimental value= 13.34 – 10.95 = 2.39 The % error: error x 100 = accepted value 2.39 x 100 = 13.34
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The error: accepted value – experimental value= 13.34 – 10.95 = 2.39 The % error: error x 100 = accepted value 2.39 x 100 = 17.9% 13.34
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Practice Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
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Practice Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0? 28.9 – 27.0 =
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Practice Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0? 28.9 – 27.0 = 1.90
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Practice Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0? 28.9 – 27.0 = 1.90 1.90/27.0 x 100% =
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Practice Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0? 28.9 – 27.0 = 1.90 1.90/27.0 x 100% = 7.04%
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Practice What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
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Practice What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C? 60.8 °C – 40.6 °C =
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Practice What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C? 60.8 °C – 40.6 °C = 20.2 °C
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Practice What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C? 60.8 °C – 40.6 °C = 20.2 °C 20.2 °C / 60.8 °C x 100% =
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Practice What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C? 60.8 °C – 40.6 °C = 20.2 °C 20.2 °C / 60.8 °C x 100% = 33.2%
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