2-2: Units of Measurement

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2-2: Units of Measurement. Objectives: Name SI units for length, mass, time, volume, and density Distinguish between mass and weight Perform density calculations Transform a statement of equality to a conversion factor. SI Measurement. Le Systeme International d’Unites Abbreviated SI

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### 2-2: Units of Measurement

Objectives:

Name SI units for length, mass, time, volume, and density

Distinguish between mass and weight

Perform density calculations

Transform a statement of equality to a conversion factor

SI Measurement
• Le Systeme International d’Unites
• Abbreviated SI
• Adopted 1960 as world-wide agreed upon standards
• Defined in terms of standards of measurements
SI Base Units
• There are 7 base units in SI
Some SI Base Units
• Mass
• A measure of the amount of matter in an object
• SI unit for mass is the kilogram (kg)
• The gram (g) is more useful for measure masses of small objects
• The milligram (mg) is used for even smaller objects
• Length
• SI standard unit for length is the meter (m)
• The kilometer (km) is used to express longer distances
• The centimeter (cm) is used to express shorter distances
Metric Prefixes
• Prefixes are added to the names of SI base units to represent quantities that are larger or smaller than the base units
Derived SI Units
• Derived units: combinations of SI base units
• Produced by multiplying or dividing standard units
• Examples:
• Area m2 length x width
• Volume m3 length x width x width
• Density

Volume

• Volume: the amount of space occupied by an object
• The derived SI unit is cubic meters (m3)
• One cubic meter = the volume of a cube whose edges are 1 m long
• Cubic centimeter (cm3) is usually used because m3 is a very large unit
• Volumes of liquids and gases are often measured by a non-SI unit called the liter (L)
• 1 L = 1000 cm3
• The milliliter (mL) is used for smaller volumes
• 1000 mL = 1 L
• 1000 mL = 1 L = 1000 cm3 1 mL = 1 cm3!

Density

• Density: the ratio of mass to volume, or mass divided by volume
• The SI unit for density is
•  Units are too large!
• Unit often used is grams or
• A characteristic physical property of a substance
• Can be used as one property to help identify a substance

m

D

V

m

m

V

D

V

D

Sample Problem
• A sample of aluminum has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of the aluminum.
• Given: mass (m) = 8.4 g volume (V) = 3.1 cm3
• Unknown: density (D)
• You know that
• Plug in the values!
You Try!
• What is the density of a block of marble that occupied 310 cm3 and has a mass of 853 g?
• 2.75 g/cm3
• Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?
• 1.14 g
• 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?
• 5.60 mL
Conversion Factors
• Conversion factor: a ratio from the equality between two different units that can be used to convert from one unit to the other
• Example:
• 1 dollar = 4 quarters or 4 quarters = 1 dollar
• or
• When you want to use a conversion factor to change a unit in a problem, you can set up the problem the following way:
• Example: How many quarters are in 12 dollars?

You can convert factors if you know the relationship between the unit you have and the unit you want!

• Example:
• deci- means “1/10”
• 1 meter (m) = 10 decimeters (dm)

AND

• deci- also means “0.1”
• 0.1 meter (m) = 1 decimeter (dm)

 You can write the following conversion factors relating meters and decimeters

Sample Problem
• Express a mass of 5.712 grams in milligrams and in kilograms.
• Given: 5.712 g
• Unknown: mass in mg and kg
• Solution:
•  mg: The expression that relates grams to milligrams is 1 mg = 0.001 g
• The possible conversion factors are
•  kg: To find kilogram is similar 1 kg = 1000 g
• The possible conversion factors are
You Try!
• Express a length of 16.45 m in centimeters and in kilometers.
• 1645 cm
• 0.01645 km

1000

Stair Step Method

100

Kilo-

10

Hecto-

Deka-

1

0.1

King

Base

Unit

0.01

Henry

Deci-

0.001

Centi-

Died

By

Milli-

Drinking

Base units:

Mass = Gram (g)

Length = Meter (m)

Volume = Liter (L)

Chocolate

Milk

You Try!
• Express a mass of 0.014 mg in grams.
• Answer: 0.000014 g