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Metric system

Some common conversion factors:

Conversions

Metric table 1
Metric table 2

1. Why do Americans use the English/Imperial system instead of the Metric system?

2. Why do we (sometimes) need to convert between Metric and English?

3. What’s the big deal? Come up with 2 examples of things that could go very, very wrong, if someone mixes up metric and English units:

Simpsons car accident

Famous examples:

The Gimli Glider

Gimli_glider

The Gimli Glider is the nickname of an Air Canada aircraft that was involved in an unusual aviation incident. On July 23, 1983, Air Canada Flight 143, a Boeing 767–233 wide body jetliner, ran out of fuel at an altitude of 12,500 metres (41,000 ft) above mean sea level, about halfway through its Montreal to Edmonton flight. The flight crew was able to glide the aircraft safely to an emergency landing at an auto racing track that was previously RCAF Station Gimli, a Royal Canadian Air Force base in Gimli, Manitoba.
The subsequent investigation revealed a combination of company failures and a chain of human errors that defeated built-in safeguards. The amount of fuel that had been loaded was miscalculated because of a confusion as to the calculation of the weight of fuel using the metric system, which had recently replaced the imperial system for use with the 767.

https://en.wikipedia.org/wiki/Gimli_Glider

Mars Climate Orbiter

Mars Climate Orbiter metric

A subcontractor used Imperial units (pound-seconds) instead of the metric units (newton-seconds) as specified by NASA.

The Vasa sinks, 1628

Sinking of the Vasa warship in 1628

Vasa stern ship

Vasa set sail on her maiden voyage on August 10, 1628. At the time, she was the most powerfully armed warship in the world, with 64 bronze cannons. Twenty minutes into her journey, the ship was hit by two strong winds. It heeled to port, water gushed in, and the ship sank less than a mile into the journey. Thirty people died.

Soon after, there was an inquest that concluded that the ship had been unstable. But the reasons behind the instability have remained a point of debate over the centuries. Fred Hocker, an archaeologist at the Vasa Museum, has been trying to find some definitive answers. “We have, over the last three years, measured every single piece of the wood in the ship,” says Hocker. “If we want to understand how the ship was built, that’s what it takes.” Hocker’s meticulous measurements paid off. They gave him fresh insight into what made the Vasa unstable. For one thing, the ship was asymmetrical, more so than most ships of the day. “There is more ship structure on the port side of the hull than on the starboard side,” explains Hocker. “Unballasted, the ship would probably heel to port.”

No wonder the ship tipped to the port side when the winds hit. But why was the ship so lopsided? While examining the ship, Hocker discovered four rulers the workmen had used. Those rulers were based on different standards of measurement at the time.  Two were in Swedish feet, which were divided into twelve inches. The other two were in Amsterdam feet, which had eleven inches in a foot. So each carpenter had used his own system of measurement. “When somebody tells him, make that thing four inches thick, his four inches is not going to be the same as the next guy’s four inches,” says Hocker. “And you can see those variations in the timbers, as well.”

http://www.pri.org/stories/2012-02-23/new-clues-emerge-centuries-old-swedish-shipwreck
http://www.bbc.com/news/magazine-27509559

Metric system funny meme

American still often use the “traditional systems of weights and measures”. It was developed from English units, used by the British Empire before American independence.

The British system of measures was overhauled in 1824 to create the Imperial system, changing the definitions of some units. So while many U.S. units are similar to their Imperial counterparts, there are now some differences between the systems.

Why didn’t we change to the Metric system, like the rest of the world?

Simpsons Metric system is the tool of the Devil

4. Show me that you know the English system

Copy this into your notes, and fill in the blanks: But don’t look the answers up: We’re testing to see if we really, truly know the English system!

1 inch (in.) = _____ feet

1 foot = __________ inches

1 foot (ft) = ____ yard

1 yard = ____ feet

1 rod (rd) = ____  yards

1 furlong = ____  yards =  _____ mile

1 mile = ______ yards = ______ feet

1 nautical mile = _____ feet

1 acre = _____________ square feet

1 tablespoon = ___________ teaspoons

1 US fluid ounce (fl oz) = _____ tabelspoons

1 pint = ________ cups

1 barrel = __________ gallons

1 hogshead = ________ gallons

1 pound = ________ ounces

1 long hundredweight = ____ pounds

1 ton = ___ pounds

Some solutions

1 inch (in.) = 1/36 yard = 1/12 foot
1 foot = 12 inches
1 foot (ft) = 1/3 yard
1 yard (yd) = 3 feet
1 rod (rd) = 5 ½ yards
1 furlong = 220 yards = 1/8 mile
1 mile = 1,760 yards = 5,280 feet
1 fathom = 6 feet
1 nautical mile = 6,076.1 feet

america rejects metric system King Henry's foot

Area

Unit Divisions SI Equivalent

Exact relationships shown in boldface

1 square survey foot (sq ft or ft2)

144 square inches

0.09290341 m2

1 square chain (sq ch or ch2)

4356 sq ft (survey) or 16 sq rods

404.6873 m2

1 acre

43560 sq ft (survey) or 10 sq ch

4046.873 m2

1 section

640 acres or 1 sq mile (survey)

2.589998 km2

1 survey township (twp)

36 sections or 4 sq leagues

93.23993 km2

Volume

Volume in general

Unit

Divisions

SI Equivalent

1 cubic inch (cu in) or (in3)

16.387064 mL[13]

1 cubic foot (cu ft) or (ft3)

1728 cu in

28.31685 L

1 cubic yard (cu yd) or (yd3)

27 cu ft

764.554857984 L

0.764554857984 m3

1 acre-foot (acre ft)

43560 cu ft

1613.333 cu yd

1.233482 ML

1233.482 m3

Unit Divisions SI Equivalent

1 minim (min)

~1 drop or 0.95 grain of water

61.611519921875 μL

1 US fluid dram (fl dr)

60 min

3.6966911953125 mL

1 teaspoon (tsp)

80 min

4.92892159375 mL

1 tablespoon (Tbsp)

3 tsp or 4 fl dr

14.78676478125 mL

1 US fluid ounce (fl oz)

2 Tbsp or 1.0408 oz av of water

29.5735295625 mL

1 US shot (jig)

3 Tbsp

44.36029434375 mL

1 US gill (gi)

4 fl oz

118.29411825 mL

1 US cup (cp)

2 gi or 8 fl oz

236.5882365 mL

1 (liquid) US pint (pt)

2 cp or 16.65 oz av of water

473.176473 mL

1 (liquid) US quart (qt)

2 pt

0.946352946 L

1 (liquid) US gallon (gal)

4 qt or 231 cu in

3.785411784 L

1 (liquid) barrel (bbl)

31.5 gal or 12 hogshead

119.240471196 L

1 oil barrel (bbl)

42 gal or 23 hogshead

158.987294928 L

1 hogshead

63 gal or 8.421875 cu ft

or 524.7 lb of water

238.480942392 L

Units of Mass

Conversions

Type

Unit

Divisions

SI equivalent

Avoirdupois

1 grain (gr)

17000 lb

64.79891 mg

1 dram (dr)

27 1132 gr or 8.859 carats

1.7718451953125 g

1 ounce (oz)

16 dr

28.349523125 g

1 pound (lb)

16 oz

453.59237 g

1 US hundredweight (cwt)

100 lb

45.359237 kg

1 long hundredweight

112 lb

50.80234544 kg

1 ton (short ton)

20 US cwt or 2000 lb

907.18474 kg

1 long ton

20 long cwt or 2240 lb

1016.0469088 kg

Troy

1 grain (gr)

17000 lb av or 15760 lb t

64.79891 mg

1 pennyweight (dwt)

24 gr or 7.776 carats

1.55517384 g

1 troy ounce (oz t)

20 dwt

31.1034768 g

1 troy pound (lb t)

12 oz t or 13.17 oz av

373.2417216 g

Most common measures shown in italics
Exact conversions shown in bold

5. We need the metric system to simplify this

Presentation on the Metric system

6. How to do Metric conversions

To convert from a smaller unit to a larger unit:

Count the number of lines up the table; move the decimal this many spaces left.

______________________________________________________

The Joker and the metric system

To convert from a larger unit to a smaller unit:

Count the number of lines down the table; move the decimal this many spaces right.

metric system table

metric system table

Palpatine Let the Metric System Flow Through You

To convert from a smaller unit to a larger unit:

1,000 grams is how many kilograms?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 grams is the same as 1 kilogram
_________________________________________________

1,000 meters is how many kilometers?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 m is the same as 1 km

_________________________________________________

1,000 liters is how many kiloliters?

Kilo is three lines up; move the decimal point three spaces to the left

1,000 ⇨ 1.000 1,000 liters is the same as 1 kiloliter

_________________________________________________
Wow! Conversions are the same in grams, meters, liters, degrees, or any other units!
_________________________________________________

1,000 μg micrograms is how many decigrams?

Deci is five lines up; move the decimal five spaces to the left.

1,000 ⇨ 0.01 1,000 μg is the same as 0.01 decigrams

_________________________________________________

25,000 microliters (also: 25,000 μL) is how many liters?

Liters has no prefix; it is the base unit line. This line is six lines up.

Move the decimal six places left.

25,000 ⇨ 0.025 liters 25,000 μL is 0.025 L

_________________________________________________

520,000 millimeters is how many kilometers?

Kilo is six lines up; move the decimal six spaces left.

520,000 mm ⇨ 0.52 km 520,000 mm is 0. 52 km

_________________________________________________

To convert from a larger unit to a smaller unit:

1,000 grams is how many milligrams?

Milli is three lines down; move the decimal point three spaces to the right.

1,000 ⇨ 1,000,000 1,000 g is 1,000,000 mg

_________________________________________________

0.05 megabytes is how many kilobytes?

Kilo is three lines down; move the decimal point three spaces right.

0.05 ⇨ 50 0.05 megabytes is 50 kilobytes

_________________________________________________

1 dekagram is how many micrograms?

Micro is seven lines down; move the decimal point seven spaces right.

1 ⇨ 1,000,000 1 dg is 10,000,000 μg

7. Converting from one system to another.

Sometimes we’ll need to convert from one system to another, for example from metric to Imperial (English.) To do that we’ll use dimensional analysis.

Dimensional analysis: KaiserScience

_________________________________________________

Learning standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Science and Engineering Practices: 5. Using Mathematics and Computational Thinking:
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).

National Council of Teachers of Mathematics
Students need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships.

National Science Teachers Association
The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International

Metric system tutorial
http://www.chemistryland.com/CHM151W/01-Foundation/Metric/Metrics151.html

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