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The Metric System Important dates in the history of the modern metric system (S.I.): 1670 metric system originated on about this date. Gabriel Mouton, a French vicar 1790 Thomas Jefferson proposed a decimal-based measurement system for the United States. 1792 The U.S. Mint was formed to produce the world's first decimal currency (the U.S. dollar consisting of 100 cents). 1866 The use of the metric system made legal (but not mandatory) in the United States by the Metric Act of 1866 (Public Law 39-183). This law also made it unlawful to refuse to trade or deal in metric quantities. 1975 The Metric Conversion Act of 1975 (Public Law 94-168) passed by Congress. The Act established the U.S. Metric Board to coordinate and plan the increasing use and voluntary conversion to the metric system. However, the Act was devoid of any target dates for metric conversion. 1979 BATF requires wine producers and importers to switch to metric bottles in seven standard [liter and milliliter] sizes. 1983 The meter is redefined in terms of the speed of light by the 17th CGPM, resulting in better precision but keeping its length the same. 1988 The Omnibus Trade and Competitiveness Act of 1988 amended and strengthened the Metric Conversion Act of 1975, designating the SI metric system as the preferred measurement system, and requiring each federal agency to be metric by the end of fiscal year 1992. 1991 President George Bush signed Executive Order 12770, Metric Usage in Federal Government Programs directing all executive departments and federal agencies implement the use of the metric system. The Executive Order is also available as an appendix to: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy 1994 The Fair Packaging and Labeling Act (FPLA) was amended by the Food and Drug and Administration (FDA) to require the use of dual units (inch-pound AND metric) on all consumer products. 1996 As of July 1996 all surface temperature observations in National Weather Service METAR/TAF reports are now transmitted in degrees Celsius. 2001 April 09 U.S. Stock Exchanges changed to decimal trading. The Securities and Exchange Commission has ordered that all stocks must be quoted in dollars and cents rather than fractions by this date. The switch to decimal trading brought the U.S. in line with the rest of the world's major exchanges. This follows the change of the Canadian Stock Exchanges to decimal trading in 1996. One of the principal advantages of the Metric System is its use of only one unit (standard of size) for each parameter (thing that is being measured). The metric units are interrelated in such a way that only five fundamental standards are necessary. These fundamental standards are identified with an * in the tables below. The 5 Standard Metric Units Second - time Gram - mass degrees Kelvin - temperature Candle - light Coulomb - electrical charge MECHANICS Parameter: Metric Unit English Units Time duration, delay second * s second, minute, hour, day frequency Hertz 1/s cycle per second length distance, displacement Meter 1/299 792 458 light sec m inch, foot, yard rod, chain, furlong, mile velocity, speed rate of change of position meter per second m/s foot per second mile per hour, knot acceleration rate of change of velocity meter per second squared m/s2 foot per second squared mass quantity of material gram * g ounce, pound, ton force push, pull, or weight Newton kg m/s2 pound-force impulse force times time newton second kg m/s pound-force second momentum mass times velocity kilogram meter per second kg m/s pound foot per second work, energy force times distance joule (pronounced "jewel") = one newton meter kg m2/s2 foot pound-force power rate of doing work Watt = one joule per second kg m2/s3 foot pound-force per second horsepower area size of a surface square meter m2 square foot, square yard acre, square mile pressure force per unit area Pascal newton per square meter kg/m s2 pound-force per square inch volume, capacity cubic meter (stere) m3 pint, quart, gallon cubic foot, cubic yard density, heaviness grams per cubic centimeter g/cm3 pounds per cubic foot HEAT Parameter: Metric Heat Unit English Heat Unit heat energy joule, calorie, Calorie 1 cal = 4.186 joules 1 Cal = 4186 joules British Thermal Unit temperature change kelvin * Fahrenheit degree temperature degrees kelvin degrees Fahrenheit LIGHT Parameter: Metric Light Unit luminous intensity candle * luminous flux lumen one candle produces 4 pi lumens illumination lux lumen per square meter focus diopter reciprocal meters astronomical distance parsec ELECTRICITY & MAGNETISM (There are no English electrical units) Parameter: Metric Electrical Unit electric charge coulomb * 96,500 coul = 1 faraday = 1 mole of electrons electromotive force (EMF) volt (joule per coulomb) capacitance farad (coulomb per volt) electric current ampere (coulomb per second) electric energy joule (watt second) -- (newton meter) KWH = 3,600,000 joules electric power watt (joule per second) electrical resistance ohm (volt per ampere) electrical conductivity siemens (coulomb per joule) (ampere per volt) electrical field strength electromagnetic inductance volts per meter henry (pl. henrys) magnetic field intensity oersted (formerly the gauss) magnetic flux weber (108 maxwells) magnetic flux density tesla weber per square meter magnetomotive force gilbert Each physical quantity (length, mass, volume, etc.) is represented by a specific SI unit. That unit is made larger or smaller by addition of a prefix to the stem unit. Commonly used metric system units and symbols: Type of Measurement Unit Name Symbol length, width, distance, thickness, girth, etc. meter m mass (often called weight) kilogram* kg mass (larger) metric ton t time second s temperature degree Celsius** °C area square meter m2 area (land) hectare ha volume (liquid or other) liter L*** volume (larger) cubic meter m3 density kilogram per cubic meter kg/m3 velocity meter per second m/s velocity (autos) kilometer per hour km/h force newton N pressure, stress kilopascal kPa energy kilojoule kJ power watt W *The gram (g) is the stem unit to which other prefixes are added. **The kelvin (K) is the SI base unit of thermodynamic temperature. ***The capital el (L) is preferred as the symbol for liter in the USA; however the lower case el (l) also is correct and is used in many metric countries. Derived Units Force Newton N kg m s-2 Energy joule J kg m2 s-2 Power watt W kg m2 s-3 Frequency hertz Hz s-1 Charge coulomb C As Capacitance farad F C2 s2 kg-1 m-2 Magnetic Induction tesla T kg A-1 s-2 The Metric Prefixes Prefix: Symbol: Magnitude: Meaning (multiply by): 24 Yotta- Y 10 1 000 000 000 000 000 000 000 000 Zetta- Z 1021 18 1 000 000 000 000 000 000 000 Exa- E 10 1 000 000 000 000 000 000 Peta- P 1015 1 000 000 000 000 000 Tera- T 10 12 1 000 000 000 000 Giga- G 109 1 000 000 000 Mega- M 6 1 000 000 4 10 myria- my 10 10 000 (this is now obsolete) kilo- k 103 1000 hecto- h 10 2 100 deka- da 10 10 - - - - deci- d 10-1 c -2 0.01 10 -3 0.001 10-6 0.000 001 centimilli- m micro- u (mu) 10 -9 0.1 nano- n 10 0.000 000 001 pico- p 10-12 0.000 000 000 001 femto- f 10 -15 0.000 000 000 000 001 atto- a 10-18 0.000 000 000 000 000 001 zepto- z -21 0.000 000 000 000 000 000 001 -24 0.000 000 000 000 000 000 000 001 yocto- y 10 10 Commonly used metric prefixes Prefix Name Prefix Symbol Prefix Value giga G 1 000 000 000 109 mega M 1 million or 1 000 000 106 kilo k 1 thousand or 1000 103 hecto h 100 102 deka da 10 10 deci d 1/10 or 0.1 10-1 centi c 1/100 or 0.01 10-2 milli m 1/1000 or 0.001 10-3 micro µ 1/1 000 000 or 0.000 001 10-6 nano N 1/1 000 000 000 or 0.000 000 001 10-9 Some special relationships: 1 milliliter = 1 cubic centimeter 1 milliliter of water has a mass of approximately 1 gram 1 liter of water has a mass of approximately 1 kilogram 1 cubic meter of water has a mass of approximately 1 metric ton Legal/official (exact) definitions of inch-pound units as set by U.S. law: 1 inch = 25.4 millimeters 1 pound = 453.592 37 grams 1 gallon = 3.785 411 784 liters Note: In Canada the inch and the pound are defined identically, but 1 Canadian gallon = 4.546 09 liters. Approximate conversion factors between inch-pound units and the International System of Units (SI): Multiply inches by 2.54 to get centimeters (this conversion factor is exact) Multiply feet by 0.305 to get meters Multiply miles by 1.6 to get kilometers Divide pounds by 2.2 to get kilograms Multiply ounces by 28 to get grams Multiply fluid ounces by 30 to get milliliters Multiply gallons by 3.8 to get liters Some baseline temperatures in the three temperature scales temperature kelvins degrees Celsius degrees Fahrenheit symbol °K °C °F boiling point of water 373.15 100. 212. average human body temperature 37. 98.6 average room temperature 20. to 25. 68. to 77. freezing / melting point of water / ice 273.15 0. 32. absolute zero 0. -273.15 -459.67 Temperature conversions between the three temperature scales: kelvin / degree Celsius conversions (exact): kelvins = degrees Celsius + 273.15 degrees Celsius = kelvins - 273.15 degree Fahrenheit / degree Celsius conversions (exact): degrees F = degrees C x 1.8 + 32. degrees C = (degrees F - 32.) / 1.8 A degree Celsius memory device: There are several memory aids that can be used to help the novice understand the degree Celsius temperature scale. One such nemoic is: When it's zero it's freezing, when it's 10 it's not, when it's 20 it's warm, when it's 30 it's hot! Or, another one to remember: 30's hot 20's nice 10's cold zero's ice Examples of everyday item equivalences for metric units of length, mass, volume, and temperature (Drawings excerpted from the book, Quick Guide to the Metric System, by Valerie Antoine, USMA Executive Director) Length: 1 meter (1 m) 1 centimeter (1 cm) 1 kilometer (1 km) Mass: 1 kilogram (1 kg) 1 gram (1 g) Volume: 1 liter (1 L or 1 l) 1 milliliter (1 mL or 1 ml) Temperature: degree Celsius (°C) Scientific Notation Learn how to write numbers in scientific notation http://www.nyu.edu/pages/mathmol/textbook/scinot.html More info http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html Temperature conversions (°C <--> °F) Sources: http://lamar.colostate.edu/~hillger/ http://users.aol.com/tspquinn/units.html http://www.essex1.com/people/speer/metric.html http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl http://www.nyu.edu/pages/mathmol/textbook/scinot.html http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html