Metric System

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Topics

• Metric System
• Conversions
• Dimensional Analysis

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If you show a good knowledge of the English
measurement system, you can skip all test
questions related to the metric system.
CHALLENGE
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FRUIT DRINKS
If these are one quart each, how many gallons are
here?
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Strawberries and other fruits are often sold in
one quart containers. Are these quarts the same
size as a quart of strawberry juice?
Dry Quart vs. Liquid Quart
Dry Quart 1.07 Liquid Quarts
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What does 8 quarts of strawberries make?
1 PECK
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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 make 1 troy pound.823 lbs
avoirdupois
These are 16 oz gloves. How many pounds do each
weigh?
The standard (Avoirdupois) pound of the United
States is equivalent to the weight of 27.7015
cubic inches of distilled water at 62o
Fahrenheit, the barometer being at 30 inches, and
the water weighed in the air with brass weights.
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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)

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MARS CLIMATE ORBITER
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Dec. 11, 1998
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Sept. 23, 1999
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• 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.

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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 Earths gravity has the
weight of 32 pounds.
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Newtons second law of motion
f ma
f 1 slug x 32 ft/sec per sec (22 mph per sec) 1
lb ? slugs x 32 ft/sec per sec 32 lbs 1 slug
x 32 ft/sec2
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Weight versus Mass
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Something has mass if it is affected by gravity.
These methods wont work in the weightlessness of
space.
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If the girls push with the same strength, one can
measure the distance the two cars moved after 5
seconds and calculate mass.
Mass resists change in motion
On level ground, gravity has no effect on the
difficulty of overcoming the mass of the cars.
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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
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Seabiscuits races like most horse races goes for
10 furlongs. How far is that?
1 furlong 1/8 mile
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What if gallons were different sizes in different
cities?
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What if clothing sizes weredifferent in
different cities?
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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.
Jefferson
Washington

• 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.

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Currency is based on 10.
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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.
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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.
Celsius
Fahrenheit
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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 Earths surface
over a few degrees, then calculate distance from
Equator to North Pole.
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A survey team was suppose to measure the distance
between Barcelona, Spain going through Paris and
up to the English Channel.
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By dividing the distance from the equator to the
north pole by 10 million, a convenient length was
defined.
Meter
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.
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40,000,000 meters
40,000 km
1 kilometer1,000 meters
10 million meters 10 million meters 10 million
meters 10 million meters
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The motto for the metric system was For all
people, for all time
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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.

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• Since we have 10 fingers, a number system
  based on 10 was developed.

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Place Value

• Roman Numerals did not take advantage of place
  value. X in Roman Numerals meant ten. XXX meant
  thirty. It didnt matter where the X was placed
  it always had the value of 10

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Modern number systems use place value. In other
words, a numeral has a different value depending
where its placed.
2222.0
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4/20/01
0.5 versus 5
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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 isjust the reverse.

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Decimal

• The word decimal from from Latin decimalis
  meaning of a tithe A tithe was traditionally
  one tenth of income, so deci- meant one tenth.
• The new measuring system should also be based on
  tens and tenths.

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Metrics Earth, water, and fingers
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10 million meters 10 million meters 10 million
meters 10 million meters
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Cubits Yards Miles Nautical Miles Feet Hands Inch
es Leagues Chains Furlongs
METER
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sq. milessq. yardssq. ft.sq. in.acres
SQUARE
METER
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BarrelCubic inchesCubic feetCubic
yardsMinimsDrops
Gallons, imperial gallons, quarts, pints, fluid
ounces, pecks, bushels
Cubic decimeter
CUBIC
LITER
METER
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1 gram defined as the mass of one cubic
centimeter of water (or one milliliter mL of
water_.
cubic centimeter
cubic decimeter
milliliter
LITER
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cubic decimeter
LITER
Liter from Litron Measure of capacity
One liter of water has a mass of one kilogram
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Force

• Push one kilogram pushed to so that it reaches
  the speed of one meter per second.
• Newton

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You are not changing the size, just the name.
CONVERSIONS
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Convert 0.15 meters to centimeters
equal
Starting amount
End Amount
centimeters
0.15 meters
1 centi
.01
0.15 meters 15 meters
15 centimeters
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If saying 15 hundredths, just say 15 centi-
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Convert 5234 millimeters to meters
equal
Starting amount
End Amount
meters
5234 millimeters
0.001
milli
5234 millimeters 5234 meters
1000
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Convert 5234 millimeters to centimeters
equal
equal
Starting amount
End Amount
centimeters
centi
5234 millimeters
0.001
milli
0.01
5234. millimeters
523.4 centimeters
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Convert 5234 millimeters to inches
Units match
equal
equal
Starting amount
End Amount
1 inch2.54 cm
2.54 cm1 inch
inches
centi
5234 millimeters
0.001
milli
0.01
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I wonder how many pennies are in 1 mega buck?
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Units Match!
1 M
1 x 108
cents
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Convert 21 grams per liter (21 g/L) to milligrams
per milliliter (mg/mL)
equal
equal
Starting amount
End Amount
21 gramsLiter
milli0.001
mgmL
0.001milli
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Convert 21 mg per liter (21 g/L) to grams per 100
cc
equal
equal
equal
Starting amount
End Amount
21 mgLiter
0.001milli
0.10.1
g 100cc
1L1000cc
0.00021
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Examples
mega- M million 1,000,000 106
kilo- k thousand 1,000 103 kilograms

deci- d tenth 1/10 0.1 10-1 dm3liter
centi- c hundredth 1/100 0.01 10-2 cmcentimetercccubic cm
milli- m thousandth 1/1000 0.001 10-3 mgmilligrammLmilliliter
micro- µ millionth 1/1,000,000 0.000001 10-6 µgmicrogram
nano- n billionth 1/1,000,000,000 0.000000001 10-9 nmnanometers
Metric facts 1 cubic centimeter 1 milliliter
(1 cc1mL)Liter 1 cubic decimeter 1,000
cubic centimeters 1,000 millilitersLower case
m stands for meter or milli. Capital L for
liter.