Chapter 1-part 2. Metric Equalities An equality states the same measurement in two different units....
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Transcript of Chapter 1-part 2. Metric Equalities An equality states the same measurement in two different units....
Metric EqualitiesMetric EqualitiesAn equality
states the same measurement in two different units.
can be written using the relationships between two metric units.
Example: 1 meter is the same as 100 cm and 1000 mm.
1 m = 100 cm1 m = 1000 mm
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Conversion FactorsConversion FactorsA conversion factor is• obtained from an equality.
• E.g Metric – U.S system
Equality: 1 in. = 2.54 cm
• written as a fraction (ratio) with a numerator and denominator.
• inverted to give two conversion factors for every equality. 1 in. and 2.54 cm
2.54 cm 1 in.
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Conversion Factors in a Conversion Factors in a ProblemProblemA conversion factor
• may be obtained from information in a word problem.
• is written for that problem only.
Example : The cost of one gallon (1 gal) of gas is $4.29.
1 gallon of gas and $4.29$4.29 1 gallon of gas
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Conversion Factors for a Conversion Factors for a Percentage, ppm, and ppbPercentage, ppm, and ppb The term percent (%) means parts per 100 parts
E.g 18% body fat by massEquality : 18 kg body fat = 100 kg body mass
Conversion factors:
18 kg body fat100 kg body mass
100 kg body mass
18 kg body fatand/or
Different mass units such as grams (g), kilograms (kg), or pounds (lb) can be used, but both units in the factors must be the same
Smaller Percents: ppm and Smaller Percents: ppm and ppbppb
Small percents are shown as ppm and ppb.
• Parts per million (ppm) = mg part/kg whole
Example: The EPA allows 15 ppm cadmium in food colors15 mg cadmium = 1 kg food color
• Parts per billion ppb = g part/kg whole
Example: The EPA allows10 ppb arsenic in public water10 g arsenic = 1 kg water
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1.7 Problem Solving1.7 Problem SolvingTo solve a problem,• identify the given unit.• identify the needed unit.
Example: A person has a height of 2.0 meters. What is that height in inches?
The given unit is the initial unit of height.
given unit = meters (m)
The needed unit is the unit for the answer.
needed unit = inches (in.)
Problem SetupProblem Setup
Unit 1 x Unit 2 = Unit 2
Unit 1Given x Conversion = Needed
unit factor unit
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ExamplesExamples
An injured person loses 0.30 pints of blood. How
many milliliters of blood would that be?
Identify the given and needed units given in this
problem.
Given unit = _______
Needed unit = _______
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ExamplesExamplesA bucket contains 4.65 L of water. Write the setup for the problem and calculate the gallons of water
in the bucket.
plan:
Equalities:
Set Up Problem:
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ExamplesExamples
A rattlesnake is 2.44 m long. How many cm long is the snake?
1) 2440 cm2) 244 cm3) 24.4 cm
How many in2 in 1.5 cm2?
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Using Two or More FactorsUsing Two or More Factors
• Often, two or more conversion factors are required to obtain the unit needed for the answer.Unit 1 Unit 2 Unit 3
• Additional conversion factors are placed in the setup problem to cancel each preceding unit.
Given unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3
Unit 1 Unit 2 12
ExamplesExamples
If a ski pole is 3.0 feet in length, how long is the ski pole in mm?
If your pace on a treadmill is 65 meters per minute,
how many minutes will it take for you to walk a
distance of 7500 feet?
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1.8 Density1.8 Density
Density
• compares the mass of an object to its volume.
• is the mass of a substance divided by its volume.
Density ExpressionDensity = mass = g or g = g/cm3 volume mL cm3
Note: 1 mL = 1 cm3
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ExampleExample
Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
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Volume by DisplacementVolume by Displacement
• A solid completely submerged in water displaces its own volume of water.
• The volume of the object is calculated from the difference in volume.
45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm3
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Density Using Volume Density Using Volume DisplacementDisplacement
The density of the zinc object is
then calculated from its massand volume. Density =
mass = 68.60 g = 7.2 g/cm3 volume 9.5 cm3
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ExamplesExamples
What is the density (g/cm3) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?
1) 0.17 g/cm3 2) 6.0 g/cm3 3) 380 g/cm3
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object
33.0 mL 25.0 mL
Sink or FloatSink or Float
• Ice floats in water because the density of ice is less than the density of water.
• Aluminum sinks because its density is greater than the density of water.
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ExamplesExamples
The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?
1) 0.614 kg
2) 614 kg
3) 1.25 kg
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ExamplesExamples
If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil?
1) 0.26 L2) 0.31 L3) 310 L
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ExamplesExamples
A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm3) are obtained from the cans?
1) 1.0 L 2) 2.0 L 3) 4.0 L
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Learning CheckLearning Check
Which of the following samples of metals will displace the greatest volume of water?
1 2 3
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25 g of aluminum2.70 g/mL
45 g of gold19.3 g/mL
75 g of lead11.3 g/mL