measurements. objective distinguish between a quantity, a unit, and a measurement standard name and...
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Measurements
MeasurementsObjective
Distinguish between a quantity, a unit, and a measurement standard
Name and use SI units for length, mass, time, volume, and density
Distinguish between mass and weight
Perform density calculations
Transform a statement of equality into a conversion factor
MeasurementsReview
MeasurementsDerived SI Units
Combinations of SI base units form derived units
o Example: pressure is measured in kg/m•s2, or pascals
MeasurementsDerived SI Units
Volume is the amount of space occupied by an object
o The derived SI unit is cubic meters, m3
o The cubic centimeter, cm3, is often used
o 1 mL = 1 cm3
MeasurementsDerived SI Units
Density is the ratio of mass to volume, or mass divided by volume
o The derived SI unit is kilograms per cubic meter, kg/m3
o g/cm3 or g/mL are also used
o Density is a characteristic physical property of a substance
mass mdensity = D =
volume Vor
MeasurementsDerived SI Units
Density can be used as one property to help identify a substance
MeasurementsDerived SI Units
Sample Problem
o A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum
MeasurementsDerived SI Units
Sample Problem Answer
o Given: mass (m) = 8.4 g volume (V) = 3.1 cm3
oUnknown: density (D)
oSolution:
mass density =
v
olume 3
3
82.
.4 g
3.7 g
1 cm/cm
MeasurementsConversion Factors
Conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other
o Example: How quarters and dollars are related
4 quarters 1 dollar1 1
1 dollar 4 quarters
0.25 dollar 1 quarter1 1
1 quarters 0.25 dollar
MeasurementsConversion Factors
Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements
Quantity sought = quantity given × conversion factor
Example: the number of quarters in 12 dollars
number of quarters = 12 dollars × conversion factor
4 quarter? quarters 12 dollars 48 quarters
1 dollar
MeasurementsConversion Factors
MeasurementsConversion Factors
Deriving Conversion Factors
You can derive conversion factors if you know the relationship between the unit you have and the unit you want
Example: conversion factors for meters and decimeters
1m 0.1m 10 dm
10 dm dm m
MeasurementsConversion Factors
MeasurementsConversion Factors
Sample Problem
o Express a mass of 5.712 grams in milligrams and in kilograms
MeasurementsConversion Factors
Sample Problem Answer
o Given: 5.712 g
o Unknown: mass in mg and kg
o Solution: mg
Possible conversion factors:
1000 mg 1 gand
g 1000 mg
1000 mg5 5. 7712 g m
g12 g
1 g = 1000 mg
MeasurementsConversion Factors
Sample Problem Answer
o Given: 5.712 g
o Unknown: mass in mg and kg
o Solution: kg
1 000 g = 1 kg
Possible conversion factors:
1000 g 1 kgand
kg 1000 g
1 kg5.712 g
10000.005
g712 kg