Topics
• Metric System
• Conversions
• Dimensional Analysis
If you show a good knowledge of
the English measurement system,
you can skip all test questions
related to the metric system.
If these are one quart each, how many
gallons are here?
Strawberries and other fruits are often sold in one quart
containers. Are these quarts the same size as a quart
of strawberry juice?
What does 8 quarts of strawberries make?
An ounce of prevention is worth a pound of cure.
• How many ounces of gold does it take to make
a pound?
12 troy ounces
• This is a cap from a RC
make 1 troy
cola bottle? How much
pound=.823 lbs
does the RC cola weigh?
avoirdupois
These are 16
oz gloves.
How many
pounds do
each weigh?
Apothecary System used in
medicine
•
•
•
•
•
Based on the weight of one grain of wheat.
20 grains make a scruple
3 scruples make a dram
8 drams make a ounce
12 ounces make a pound (troy pound)
Dec. 11, 1998
Sept. 23, 1999
• The loss of the the Mars Climate Orbiter on September
23, 1999, was a most unfortunate and highly avoidable
event.
• The cause of the mishap has been traced to a mix-up
over units. Preliminary findings indicated that one team
used English units (e.g., inches, feet and pounds) while
the other used metric units for maneuvers required to
place the spacecraft in the proper Mars orbit.
• The 'root cause' of the loss of the spacecraft was the
failed translation of English units into metric units.
• For nearly three centuries, engineers and scientists
have been struggling with English units.
In weightlessness 454 grams is still 454
grams; however, 1 pound will be zero
pounds in zero gravity.
• What is the English unit for mass?
In the English system the unit for mass is the slug.
One slug sitting in Earth’s
gravity has the weight of
32 pounds.
Weight versus Mass
Air conditioner rated at 18,000 BTU per hour.
What does BTU stand for and what does it measure?
British Thermal Units = Energy to raise or lower 1 pound
of water 1 degree Fahrenheit
Seabiscuit’s races like
most horse races goes
for 10 furlongs. How
far is that?
What if gallons were different
sizes in different cities?
What if clothing sizes were
different in different cities?
In his first annual
message to Congress
(1790 January), President
George Washington
pressed for uniformity in
currency, weights, and
measures. Secretary of
State Thomas Jefferson
urged Congress to reduce
the existing separate
systems of dry and liquid
measures to one set of
measures.
Over 200 years later, we still have separate systems. For example, our dry
quart is larger than our liquid quart, so four cups of flour and 4 cups of milk
should be measured with separate measuring devices-which differ in size!
Jefferson's second plan put before Congress was to reduce every branch
[of measurement] to the same decimal ratio already established for coin, and
thus bring the calculations of the principal affairs of life within the arithmetic of
every man who can multiply and divide plain numbers.
Congress took no action. Washington urged action again in his second
annual message to Congress (1790 December 08) and the House referred the
matter to the Senate, whose committee in this matter declined (1791 March 01)
due to negotiations in progress with the French and British Governments to
obtain an international standards of measurements.
Currency is
based on 10.
In the same year of
1790 King Louis XVI
of France was also
weary of the
inconsistencies of
measurement that
was hurting trade.
He ordered a new
system of
measurements be
developed.
Earlier in that century, Fahrenheit and Celsius used water as
the basis of their thermometers. Their thermometers were
calibrated using water, which everyone had access to. This
made their thermometers useful.
Everyone
has access
to the Earth,
so this new
system was
to be based
on the size
of the Earth.
The idea was to measure a part of
Earth’s surface over a few degrees,
then calculate distance from Equator to
North Pole.
A survey team was suppose to measure the
distance between Barcelona, Spain going through
Paris and up to the English Channel.
By dividing the distance from the equator to the
north pole by 10 million, a convenient length was
defined.
Equator to North Pole
10,000,000
It was a little longer than a yard, and the name
would be from the Greek word, Metron,
meaning to measure.
The motto for
the metric
system was:
“For all people,
for all time”
Based on 10 & using Arabic Numerals
Since the number system in use was no longer
Roman Numerals, but the decimal number system
borrowed from the Arab worlds and from India, the
measurement system should also be based on 10 to
make conversions easy.
Since we have 10
fingers, a number
system based on
10 was developed.
Place Value
Roman Numerals did not
take advantage of place
value. X in Roman
Numerals meant ten. XXX
meant thirty. It didn’t
matter where the X was
placed; it always had the
value of 10
Modern number
systems use
place value. In
other words, a
numeral has a
different value
depending
where it’s
placed.
4/20/01
0.5 versus 5
Multiplying & Dividing by 10
• Because of place value, we can multiply
by ten by moving all digits to the left (or
you can look at it as the decimal point
moving to the right.)
• 25. x 10 = 250.
• Dividing by 10 is
just the reverse.
Decimal
• The word decimal from from Latin
decimalis meaning “of a tithe” A tithe was
traditionally one tenth of income, so decimeant one tenth.
• The new measuring system should also be
based on tens and tenths.
Cubits
Yards
Miles
Nautical Miles
Feet
Hands
Inches
Leagues
Chains
Furlongs
sq. miles
sq. yards
sq. ft.
sq. in.
acres
Gallons, imperial gallons, quarts,
pints, fluid ounces, pecks, bushels
Barrel
Cubic inches
Cubic feet
Cubic yards
Minims
Drops
1 gram defined as the mass of one cubic centimeter of
water (or one milliliter [mL] of water_.
Liter from Litron:
Measure of
capacity
One liter of
water has a
mass of one
kilogram
Force
• Push one kilogram pushed to so that it
reaches the speed of one meter per
second.
• Newton
You are not changing the
size, just the name.
Convert 0.15 meters to centimeters
Starting amount
0.15 meters
equal
1 centi
End Amount
=
centimeters
.01
0.15 meters = 15 meters = 15 centimeters
100
If saying 15 hundredths, just say 15 centi-
Convert 5234 millimeters to meters
Starting amount
equal
5234 millimeters
0.001
End Amount
=
meters
milli
5234 millimeters
5234 meters
1000
Convert 5234 millimeters to
centimeters
equal
equal
5234 millimeters 0.001
milli
centi
Starting amount
End Amount
=
0.01
5234. millimeters
523.4 centimeters
centimeters
Convert 5234 millimeters to inches
equal
equal
5234 millimeters 0.001
milli
centi
1 inch
2.54
cm =
0.01
2.54
cm
1 inch
Starting amount
End Amount
inches
I wonder how many
pennies are in
1 mega buck?
Units Match!
1 M$ 1 x 10 6
M
100 cents
$
=1
x 108
cents
Convert 21 grams per liter (21 g/L)
to milligrams per milliliter (mg/mL)
Starting amount
21 grams
Liter
equal
equal
milli
0.001
milli
0.001
End Amount
=
mg
mL
Convert 21 mg per liter (21 g/L) to
grams per 100 cc
Starting amount
21 mg
Liter
equal
equal
0.001
1L
1000cc
milli
equal End Amount
0.1 =
0.1
g
100cc
0.00021
Examples
megakilo-
M million
k thousand
1,000,000
1,000
106
103
decicenti-
d
c
1/10 = 0.1
1/100 = 0.01
10-1
10-2
milli-
m thousandth
1/1000 = 0.001
10-3
micro-
µ millionth
1/1,000,000
= 0.000001
10-6
dm3=liter
cm=centimeter
cc=cubic cm
mg=milligram
mL=milliliter
µg=microgram
nano-
n
1/1,000,000,000
= 0.000000001
10-9
nm=nanometers
tenth
hundredth
billionth
kilograms
Metric facts: 1 cubic centimeter = 1 milliliter (1 cc=1mL)
Liter = 1 cubic decimeter = 1,000 cubic centimeters = 1,000 milliliters
Lower case “m” stands for meter or “milli”. Capital “L” for liter.