national standards

 

International System of Units

 

While Metrication in the United States has not been completely successful, "SI" measurement is used in ALL sciences.

The International System of Units, universally abbreviated SI (from the French Le Systeme International d'Unites), is the modern metric system used in all scientific measurement.

The SI was established in 1960 by the 11th General Conference on Weights and Measures (CGPM). The CGPM is an intergovernmental organization created by a diplomatic treaty called the Meter Convention (Convention du Metre, often called the "Treaty of the Meter" in the United States). The Meter Convention, signed in Paris in 1875 by representatives of seventeen nations (including the United States) remains the basis of all international agreement on units of measurement.

The Meter Convention also created the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures) and the International Committee for Weights and Measures (CIPM, Committee International des Poids et Mesures). The BIPM, which is located in Sevres, a suburb of Paris, France, and which has the task of ensuring worldwide unification of physical measurements, operates under the exclusive supervision of the CIPM, which itself comes under the authority of the CGPM.

There are a number of rules and style conventions for the use of the SI. These ensure that scientific and technical communication is not hindered by ambiguity. A complete description of these rules and style conventions are found in NIST Special Publication 811. Common rights and wrongs are at the bottom of this page.

 

Definitions of SI Base Units
 
Base Unit Original Definition   Modern Definition
Length - meter (m) 1/40 000 000 of Earth's polar circumference  The distance light travels in a vacuum in 1/299 792 458 of a second.
Mass - kilogram (kg)   mass of a liter (dm3) of water The mass of the International Prototype Kilogram, a small cylinder of platinum-iridium preserved in a vault in France.
Time - second (s) 1/86 400 of a mean solar day in the year 1900 The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom (at a temperature of 0 K).
Temperature - kelvin (K) Celsius degrees above absolute zero The fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Electric Current - ampere (A)coulomb per second (C/s); C = 6.24 x 1018 e, where e is the charge on a single electron or protonThat constant current which, if maintained in two straight parallel conductors of infinite length and negligible circular cross section, and placed one meter apart in vacuum, would produce between those conductors a force of 200 nanonewtons per meter of length.
Amount of Substance - mole (mol) g/u
[the number of atomic mass units in a gram]
As many elementary entities as there are atoms in 12 grams of carbon 12. The elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
Light Intensity - candela (cd)   brightness of a standard candle The luminous intensity in a given direction of a source that emits 1/683 watt per steradian of monochromatic radiation at a frequency of 540 THz.

 

Base units are multiplied by 10s using the following prefixes.
The shaded SI prefixes in the table below will be commonly found in science measurements:

Symbol   Prefix  
Name
Power  
of Ten  
Ordinary Notation    U.S. Name
   Yyotta1024 1 000 000 000 000 000 000 000 000
   Zzetta1021 1 000 000 000 000 000 000 000
   Eexa1018 1 000 000 000 000 000 000
   Ppeta1015 1 000 000 000 000 000
   Ttera1012 1 000 000 000 000trillion
   Ggiga109 1 000 000 000billion
   Mmega106 1 000 000million
   kkilo103 1 000thousand
   hhecto   102100  hundred
   dadeka 10110  ten
100 1one
   ddeci 10-10.1 tenth
   ccenti 10-20.01 hundredth
   mmilli10-3 0.001thousandth
   µmicro10-6 0.000 001millionth
   nnano10-9 0.000 000 001billionth
   ppico10-12 0.000 000 000 001trillionth
   ffemto10-15 0.000 000 000 000 001
   aatto10-18 0.000 000 000 000 000 001
   zzepto10-21 0.000 000 000 000 000 000 001
   yyocto10-24 0.000 000 000 000 000 000 000 001

 

Examples of Mass:

Common Multiples of Kilogram
Symbol  Name Equivalent  Approximation
 Pgpetagram1012 kg mass of 1 km3 of water
 Tgteragram109 kg mass of 1 hm3 of water
 Gggigagram106 kg mass of 1 dam3 (1000 m3) of water
 Mgmegagram (metric ton)103 kg mass of 1 m3 of water
 kgkilogram base unit mass of 1 dm3 (L) of water
 ggram 10-3 kg mass of 1 cm3 (mL) of water
 mgmilligram 10-6 kg mass of 1 mm3 (µL) of water
 µgmicrogram 10-9 kg

 

Examples of Length:

Derived Units are combinations of base units.

  • Area = length2 = (length) (width)

    Multiples of the square meter make nesting squares. Note that as you go from one square to the next larger, the sides (prefixes) increase 10 or 100 times, but the area increases 100 or 10 000 times (because 102 = 100 and 1002 = 10 000).

    Common Multiples of Square Meter
    Symbol  Name Equivalent
     Mm2square megameter 1012 m2 = 1 000 000 km2
     km2square kilometer 106 m2 = 100 ha = 100 hm2
     hm2 (ha) square hectometer (hectare) 104 m2 = 10 000 m2
     m2square meter 100 m2 = 10 000 cm2
     cm2square centimeter 10-4 m2 = 100 mm2
     mm2square millimeter 10-6 m2

  • Volume = length3 = (length) (width) (height)

    These common volume relationships are important:
    1 liter = 1 cubic decimeter (dm3)
    1 cubic centimeter (cm3) = 1 milliliter (ml)

    Multiples of the cubic meter make nesting cubes. Note that as you go from one cube to the next larger, the sides (prefixes) increase ten times but the volume increases 1000 times (because 103 = 1000).

     
    Common Multiples of Cubic Meter
    Symbol  Name Equivalent  Examples
     km3cubic kilometer 109 m3mountain
     hm3cubic hectometer 106 m3large building
     dam3cubic dekameter 103 m3large house
     m3cubic meter 100 m3desk
     dm3 (L)cubic decimeter (liter) 10-3 m3 bottle
     cm3 (mL)cubic centimeter (milliliter) 10-6 m3 bean
     mm3 (µL)   cubic millimeter (microliter) 10-9 m3 sand grain

    Multiples larger than cubic kilometer or smaller than cubic millimeter are rarely used because of the large number of placeholding (non-significant) zeros that can result. The alternative names liter, milliliter, and microliter and their symbols are holdovers from an older version of the metric system. They are acceptable for use with SI.
  • Density = mass / volume
The density of water is 1 gram per cubic centimeter (at 4 oC).
 

An Approximate Comparison of the SI and English Systems


English SystemMetric System
1 yard0.9 meter
1 mile1.5 kilometer
1 pound0.5 kilogram
1 quart
4 quarts = 3.8 liters
~1 liter

 
Temperature Scales

  • The zero point on the Kelvin scale is absolute zero, the lowest possible temperature. This is the point at which all molecular motion stops.
  • The zero point on the Celsius scale equals the melting/freezing point of water at 1 atmosphere of pressure. It is equal to 273 Kelvin units and 32 degrees Fahrenheit.
  • The zero point on the Fahrenheit scale is based on the freezing point of a mixture of salt and water and scientifically meaningless.
  • The boiling point of water at 1atmosphere of pressure is set to 100 degrees on the Celsius scale.
  • The interval between the melting point and the boiling point of water is divided into 100 intervals, each equal to 1 degree. This interval is the same on the Kelvin scale. 1 Kelvin unit = 1 degree Celsius.
  • When working with the Kelvin scale, the term "degrees" is not used. Zero degrees Celsius is written as 273 K and read as "273 Kelvins".
  • The Fahrenheit scale is not used in science.
 
Temperature Conversions:

  1. Convert from the Celsius scale to the Kelvin scale:

    The conversion equation is   oC + 273 = K

    Example: convert 37o Celsius to Kelvins.

    C + 273 = K

    37 + 273 = 310K

  2. Convert from the Kelvin scale to the Celsius scale:

    The conversion equation is   K - 273 = oC

    Example: convert 300 Kelvins to o Celsius.

    K - 273 = C

    300 - 273 = 27 oC

temperature scale comparison

Since Fahrenheit temperatures are not used in science, there is common need for conversions using it. However, the following equations can be used for Fahrenheit conversions:

3. Converting from the Celsius scale to the Fahrenheit scale:
The conversion equation is   9/5 C + 32 = oF

Example: convert 37o Celsius to Fahrenheit.

9/5 C + 32 = oF

( 9/5 X 37 ) + 32 = 98.6oF.

9/5 = 1.8, meaning that 1 degree on the Celsius scale = 1.8 degrees on the Fahrenheit scale. Look at the picture of the three scales above: a five degree interval on the Celsius scale equals a nine degree interval on the Fahrenheit scale.
Remember, 37oC equals 98.6oF, because it is the body temperature.

4. Converting from the Fahrenheit scale to the Celsius scale:

The conversion equation is   (F - 32) / 9/5

Example: convert 98.6 oF to Celsius.

(F - 32) / 9/5
(98.6 - 32) / 9/5 = 37 oC

First subtract 32, then divide by 1.8. Instead of dividing by 1.8, you may also multiply by 5/9.

 

Correct Use of SI Symbols

SI is the abbreviation for the Systeme International d'Unites. (Do not abbreviate it as S.I.)

Some correct and incorrect examples of its usage are shown below. These correct ways to use SI are set by the international standards that define the SI.

  1. The short forms for SI units (such as mm for millimeter) are called symbols, not abbreviations.

  2. SI symbols never end with a period unless they are the last word in a sentence.

    • RIGHT: 20 mm, 10 kg
    • WRONG: 20 mm., 10 kg.

  3. SI symbols should be preceded by digits and a space must separate the digits from the symbol.

    • RIGHT: It was 300 mm wide. The millimeter width was given.
    • WRONG: It was 300mm wide. The mm width was given.

  4. Symbols always are written in the singular form (even when more than one is meant).

    • RIGHT: 1 mm, 500 mm, 1 kg, 36 kg
    • WRONG: 500 mms, 36 kgs

    • BUT: It is correct to pluralize written-out metric unit names: 25 kilograms, 250 milliliters

  5. The symbol for a compound unit that is a quotient of two units is indicated by a solidus or by a negative exponent.

    • RIGHT: km/h or km·h-1 (for kilometers per hour)
    • WRONG: kmph or kph (do not use p as a symbol for "per".)

    • BUT: It is correct to say or write "kilometers per hour".

  6. The meaning of an SI symbol can be changed if you substitute a capital letter for a lower case letter.

    • RIGHT: mm (for millimeter, which means 1/1000 of a meter)
    • WRONG: MM or Mm (M is the prefix for mega, which means one million; a megameter is a million meters)