Measurement
Mr. Martin
1. Distance (Length)
How wide is the floppy disk?
How wide is the black metal tab?
Measure Accurately
Measuring Length of Book
Zero mark at one edge of book.
Read measurement at other edge.
Here you can read to the nearest tenth of a cm.
Breaking News!
•King Hector died
Monday drinking
chocolate milk!
King Hector died Monday drinking chocolate milk.
Kilo hecto deca meter deci
centi
milli
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Kilometer (km)
Hectometer (hm)
Decameter (dam)
Meter (m)
Decimeter (dm)
Centimeter (cm)
Millimeter (mm)
Micrometer (um)
Nanometer (nm)
1000m
100m
10m
1m
.1m
.01m
.001m
.000001m
.000000001m
You try and measure some
distances.
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Width of table in cm? in meters? in decimeters?
Length of table in cm? in meters? in decimeters?
Width of Pre-Algebra math book in cm? in meters?
Length of Pre-Algebra math book in cm? in meters?
Depth of Pre-Algebra math book in cm? in mm?
Dimensions (length and width) of floor of room in
meters?
• Length of pencil? (You choose appropriate metric
measure)
• Diameter of a coin? (You choose the coin and the
appropriate metric measure)
Conversions
(Why King Hector is important!)
• King Hector died Monday drinking chocolate milk!
• K
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C
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You Try!
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5.75m = _____ cm
5.8km = _____ m
1,345cm = _____m = _____ dam = ____dm
52cm = _____m = ______km
127mm = _____ cm = _____m = ______dm
0.056km = _____m = _____cm
2. Area
• Definition – Number of square units that fit
into a two dimensional space.
7cm
5cm
Area = 5cm x 7cm
= 35 cm2 = 35 square
centimeters
Area Applications
• The square feet in a house.
– In metric, the square meters in a house.
• The square feet of carpet in the
classroom.
– In metric, the square meters of carpet in the
classroom.
– Calculate it!
• The area in square centimeters of the
cover of the Pre-Algebra book.
– Calculate it!
Big Areas
• Large areas of land in the United States are
frequently measured in acres.
– One square mile, which is called a section, has 640
acres. Therefore, one acre is 1/640 of a square
mile.
– One mile = 5280 feet. One square mile is hence
equal to 5280 feet x 5280 feet = 27878400 square
feet. One acre is 1/640 times 27878400 = 43,560
square feet.
• Large areas of land in the metric system are
measured in Hectares.
• 1 hectare is equal to 10,000 square meters (100 meters x
100 meters)
• 1 hectare is about 2.5 acres
3. Volume
• Definition volume – the amount of three
dimensional space an object occupies.
– Measured in cubic units such as cubic meters,
cubic centimeters, etc.
1cm
1cm
1m
1cm
One Cubic
1cm
Meter
One Cubic Centimeter
(cm3)
1m
1m
What’s the volume?
Calculate it!
• Answer?
5cm
– 140 cm3
4cm
7cm
• Answer?
10m
7m
4m
– 280m3
The cube is one decimeter by one
decimeter by one decimeter
• What is the volume in
cubic decimeters?
1 dm3
• What is the volume in
cubic centimeters?
• Clue: What are the
dimensions in cm?
10cm x 10cm x 10cm =
1,000 cm3
Some Interesting Volume Names
• 1 cubic decimeter = 1,000 cubic centimeters = 1
Liter (L)
• 1 cubic centimeter (cm3) is abbreviated in
medicine frequently as cc.
• 1 cm3 = 1 cc = 1 milliliter = 1 mL
• 1 mL of water at standard temperature and
pressure has a Mass of 1 gram (gm)
• 1 L of water at standard temperature and
pressure has a Mass of 1 kilogram (Kg)
– More on Mass later
Practice with Metric Volume
• Find the volume of the classroom in:
– Cubic meters
– Liters (Remember a liter is a cubic decimeter)
– Milliliters (Remember a mL is a cubic cm)
King Hector died Monday drinking
chocolate milk! (Again!)
• King Hector is useful for converting metric units of
volume also
• King Hector died Monday drinking chocolate milk!
• K
H
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You Try!
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57.5L = _____ dL (deciliter)=_____mL
5.2mL = ____ cc = ____ cm3
5.8m3 = _____ L
1,345mL = _____L = _____ dL
52kL = _____L
.05L = ____ mL
1mL = ____L
Date: _________________
Homework
Name: ________________
1. Use a tape measure to measure the
dimensions of your bedroom. Use 2.5m
for the height of the room. (I don’t want
you climbing!) Ans. ______________
2. What is the area of the floor in square
meters? ________________________
3. What is the area of any one of your walls
in square meters? _________________
4. What is the volume of your room in cubic
meters? ___________ In liters? _______
Common Places Where Volume is
Used
• Diet Coke can
holds 355 mL of
Diet Coke
• Water bottle
holds 500 mL or
0.5 L of water
In chemistry, we can measure volume
with a flask, beaker or more accurately
with a graduated cylinder
Graduated
cylinder
beaker
Erlenmeyer
flask
Volume from Geometry
• Coke can has inner
diameter of about
6.1cm and a height of
about 12 cm
• It is roughly a cylinder
• Area = area base x
height = Πr2h =
3.14x3.05cmx3.05cmx
12cm= 351 cm3, which
is close to what the
Coke can says
Volume from Graduated Cylinder
• Or pour the
liquid into a
graduated
cylinder
How do I find the volume of the rock?
Ideas?
• Does this give
you an idea?
• It reads 200 mL
at the bottom of
the meniscus.
• How does this
help in finding
the volume of
the rock?
What do I do with the rock?
• Put rock in water
• See how much water it
displaces
• That equals the volume of the
rock
• Here, the original volume of the
water was 200mL
• The new volume is about
245mL
• The volume of the rock is
245mL – 200mL = 45mL
4. Mass
• Mass- the measure of the amount of matter in an
object
• Root prefix unit is gram (In SI the base unit is
kilogram. A gram is 1/1000 of a kilogram.)
• King Hector died Monday drinking chocolate milk
• kilo hecto deca (gram) deci
centi
milli
• As a practical matter, people primarily use kilogram
(1,000 grams), grams and milligrams (.001 gram or
1/1,000 of a gram)
• Informally, a kilogram is about 2.2 pounds, a paper clip
has a mass of about 1 gram and a new penny has a
mass of about 2.5 gram. Milligrams are very small and
are frequently used to measure the mass of
medicines.
Mass versus Weight
• In everyday language, people often use mass and
weight interchangeably. They are different, however.
• Weight is the mass of an object multiplied by its
acceleration due to gravity. Weight is a force. In the
metric system it is measured in Newtons. In customary
units it is measured in pounds.
• Your mass is same on earth as it is on the moon.
• Your weight on earth is different from your weight on
the moon since there is less gravity on the moon. If I
weigh 100 pounds on earth, I would weigh only 16.6
pounds on the moon. I would weigh 236.4 pounds on
Jupiter. (http://www.exploratorium.edu/ronh/weight/)
How to Measure Mass
• Mass is measured with a balance like the
simple balance or triple beam balance below
Simple Balance
Triple Beam Balance
Measuring Mass with Triple Beam Balance
• Set object on pan
• Move largest mass (middle) to point just before
balance tips
• Move mass in back to point just before balance tips
• Move smallest mass (front) until line is exactly at zero
A Scale Measure Weight, Not Mass
• The spring scale here technically
measures weight, not mass
• Weight is a force that is equal to the
mass times the acceleration of gravity
• This scale will show different weights
on earth and the moon. A balance will
give the same measure of mass.
• The metric unit for weight is a Newton
• This spring scale actually reads in
grams, however, a unit of mass. It is
a reasonably accurate measure of
mass on earth.
A Digital Scale
A digital scale is fast and easy
to use.
• While technically a
scale that measures
weight, this is set up
to measure mass in
grams also
• It would not give an
accurate mass on
the moon
• Here, the rock has a
mass of 115 grams
• It is precise to the
nearest gram
5. Density
• Density is mass divided by volume
• I.e., density is mass per unit volume
• A measure of density is grams/mL
Each is about the same volume.
Golf Ball
Table Tennis Ball
Which one has the greater density?
Let’s find the density of each.
4
Volume of sphere =  r 3
3
Table Tennis Ball
• Diameter of table tennis
ball is: __________
• Find volume: ________
• Mass of table tennis ball
is: ______________
(Use balance to measure)
• Density = Mass/Volume
• Make sure you have
appropriate units in the
result
Golf Ball
• Diameter of golf ball is:
__________
• Find volume: ________
• Mass of golf ball is:
______________
(Use balance to measure)
• Density = Mass/Volume
• Make sure you have
appropriate units in the
result
Measuring the Mass with Triple
Beam Balance
Let’s see the result
Table Tennis Ball
• Diameter of table tennis
ball is: 3.6 cm
• Find volume:
4
(3.14)(1.8cm)3  24.43cm3
3
Golf Ball
• Diameter of golf ball is:
4.0 cm
• Find volume:
• Mass of table tennis ball
is: 2.6g
• Density = Mass/Volume
2.6g/24.43mL =
0.106g/mL
• Mass of golf ball is:
46.0g
• Density = Mass/Volume
46.0g/33.51mL =
1.37 g/mL
4
(3.14)(2.0cm)3  33.51cm3
3
The golf ball is almost 13 times more dense. (1.37/.106 =12.9)
You Do It!
Determine the density of the tennis
ball and baseball.
Find the density of each.
4
Volume of sphere =  r 3
3
Tennis Ball
• Diameter of tennis ball is:
__________
• Find volume: ________
• Mass of tennis ball is:
______________
(Use balance to measure)
• Density = Mass/Volume
• Make sure you have
appropriate units in the
result
Baseball
• Diameter of baseball is:
__________
• Find volume: ________
• Mass of baseball is:
______________
(Use balance to measure)
• Density = Mass/Volume
• Make sure you have
appropriate units in the
result
6. Temperature
• How hot or cold a
substance is
• A measure of the
average kinetic energy
of an object
• Two common scales to
measure – Celsius and
Fahrenheit
• Celsius is used in
science and in
countries using the
metric system
100ºC
Water
212ºF Boils
0ºC
32ºF Water
Freezes
Celsius
Fahrenheit
Converting from Fahrenheit to Celsius
and Celsius to Fahrenheit
If you know the Celsius
temperature, you can convert
to Fahrenheit by plugging in
the Celsius temperature in this
formula.
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F  C  32
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The same formula in decimal
form.
F  1.8C  32
If you know the Fahrenheit
temperature, you can convert
to Celsius by plugging in
the Fahrenheit temperature
in this formula.
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C  ( F  32)
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It’s good to know at least the top formula since they show up on standardized tests.
If you know the top formula, you can also solve for C to get the bottom formula.
If you are familiar with the slope intercept form of a
line, you can figure out the formulas.
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