The International System of Units

James Richard Fromm


Quantitative measurement is the cornerstone of modern science, but it has not always been so; the application of quantitative measurements to chemistry, for example, does not predate AD 1500. Quantitative measurement was developed for other purposes, as technology, and was only then adopted for scientific use. The system of weights and measures were developed on an ad hoc basis in different parts of the world. The most fundamental quantities measured were mass or weight, length or distance, and time. Systems of units for measuring these were developed from the very beginning of recorded history. Measurement of temperature was added in the sixteenth century, and measurement of electric current in the eighteenth century. More recently amount of substance and luminous intensity have been added in the International System of Units, or SI.

The International System of Units or Systeme Internationale (SI) is an improved metric system adopted by the Eleventh General Conference of Weights and Measures in 1960. It is the universal measuring system used in all areas of science throughout the world. The entire SI system of measurement is constructed from seven base units, each of which represents a single physical quantity as shown in the table below.


Table: Base Units of the International System
Quantity Name of Unit Unit Symbol
length meter (metre) m
mass kilogram kg
time second s
temperature kelvin K
amount of substance mole mol
electric current ampere A
luminous intensity candela cd

Like earlier versions of the metric system, the SI units can be designated as decimal fractions or multiples by the use of appropriate prefixes. The acceptable SI prefixes are given in the table below.


Table: Prefixes of the International System

Prefixes for SMALL quantities:

Number Prefix Sysmbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro u (mu)
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y

Prefixes for LARGE quantities:

Number Prefix Symbol
101 deca da
102 hecto h
103 kilo k
106 mega M
109 giga G
1012 tera T
1015 peta P
1018 exa E
1021 yotta Y
1024 zetta Z

Whenever exponents are used with SI prefixes on either base units or derived units, the exponent applies to the prefix as well as to the unit. For example, nm2, or square nanometre, is interpreted as (nm)2 rather than n(m2).

Any prefix can be applied to any base unit except the kilogram; the kilogram takes prefixes as if the base unit were the gram. As a consequence 10-6 kg is written as 1 milligram (mg) rather than 1 microkilogram. Luminous intensity is rarely used in chemistry and we will not consider it further, but the remaining six base units are essential to chemical studies.

The great advantage of the SI over other systems of units is that when any physical quantity whatever is written out in the SI base units or in units derived only from the SI base units, any mathematical manipulations performed with them will follow the quantity calculus. No conversion factors will ever be required. This means that if the symbols in any equation are replaced by real numbers with their SI base units and algebraic manipulations are performed upon the units in exactly the same way as they are performed upon the numbers to which those units refer, the result will come out with the correct numbers and units.


Example. The mass of a sample of pure rhombic sulfur was 150.637 g and the volume of water it displaced was 72.8 mL. The density of sulfur is then (150.637 g)/(72.8 mL) = 2.07 g/mL, or g/cm3, or kg/dm3, or kg/L. This is 2.07(0.001 kg/g)(10+6 cm3/m3) = 2.07 x 10+3 kg/m3.

Using the quantity calculus, the mass was 0.150637 kg and the volume was 72.8 x 10-6 m3. The density of sulfur is then (0.150637 kg)/(72.8 x 10-6 m3) = 2.07 x 10+3 kg/m3. The quantity calculus gives the result in SI base units without conversion. Reporting the answer as 2070 kg/m3, while arithmetically correct and in SI base units, would give the answer to one more significant figure than is justifiable from the measured data, as will be discussed in another section.


Base Units of the SI

Length

The SI unit of length is the metre or meter, a fundamental unit of the SI. The metre was once defined in terms of the circumference of the earth as part of the older metric system. Since 1983 the metre is by definition the length of the path travelled by light in vacuum in 1/299792458 of a second. The micron is an obsolete name for the micrometre. Conversion factors between other units of length and the metre are:

1 Angstrom = 10.0 nm (exactly); 1 inch = 25.4 mm (exactly); 1 foot = 0.3048 m (exactly); 1 yard = 0.9144 m (exactly); 1 mile = 1.609344 km (exactly); 1 astronomical unit (A.U.) = 149.51 +/- 0.05 Gm

Mass

The SI unit of mass is the kilogram, a fundamental unit of the SI. The kilogram was once defined as the mass of one cubic decimetre of water. Since 1901 it is by definition the mass of the international prototype of the kilogram, a platinum-iridium mass which is stored at Sevres in France. The metric tonne is a common name for the megagram (Mg). Conversion factors between other units of mass and the kilogram, or its subdivision the gram, are:

1 unified atomic mass unit (u) = 1.66... yg; 1 pound (lb) = 453.59237 g (exactly); 1 ton (short, 2000 lb) = 907.18474 kg (exactly); 1 ounce = 1/16 lb = 28.348523... g

Time

The SI unit of time is the second, a fundamental unit of the SI. Originally defined in terms of the rotation of the earth, the second is now defined in terms of atomic transitions in 133-cesium because these are subject to more precise measurement. Specifically, since 1967 the second is defined as the duration of 9 192 631 770 periods of the electromagnetic radiation corresponding to the transition between the two hyperfine levels of the ground state of the 133-cesium atom. Conversion factors between other units of time and the second are:

1 minute = 60 s (exactly); 1 hour = 60 min = 3600 s (exactly); 1 day = 24 hr = 86.4 ks (exactly); 1 week = 7 days = 604.8 ks (exactly)

1 month (28 d) = 2.5056 Ms (exactly); 1 month (29 d) = 2.5920 Ms (exactly); 1 month (30 d) = 2.6784 Ms (exactly); 1 month (31 d) = 2.7648 Ms (exactly)

1 year (normal, 365 d) = 31.5360 Ms (exactly); 1 year (leap, 366 d) = 31.6224 Ms (exactly); 1 year (sidereal) = 31.55815... Ms

Temperature

The SI unit of temperature is the kelvin, a fundamental unit of the SI. Since 1967, the kelvin has been by definition the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The triple point of water is the temperature at which ice, water, and water vapor can all exist in equilibrium and its value is +0.01o Celsius.

The kelvin (which is correctly written without a degree sign) is used for measuring both temperature and temperature interval; thus one can say, "The temperature is 300 K" or "This pan is 20 K hotter than that one." Temperatures in kelvin can only be positive and so they require no sign. The kelvin scale of temperature is also known as the absolute scale and the thermodynamic scale. Conversion factors between temperatures in degrees Fahrenheit (oF) and in degrees Celsius (oC) and temperatures in kelvin are:

temperature (oC) + 273.15 (exactly) = temperature (K)

temperature 5/9(oF-32) + 273.15 = temperature (K)

The degree Celsius, the unit of the common metric temperature scale, is not part of the SI but its use is not discouraged. A temperature interval in degrees Celsius is identical to a temperature interval in kelvin, although a temperature in degrees Celsius is not identical to a temperature in kelvin.

Amount of Substance

The SI unit of quantity or amount of substance is the mole, a fundamental unit of the SI. There are no other modern units in which amount of substance is measured, so no conversion factors are required. Often, however, units of mass or volume are used to give the amount of substance. Conversion of these to the mole requires the use of appropriate measured physical constants, the molar mass or the molar volume. Since 1971, by definition one mole of entities is the same number of entities as there are atoms of carbon-12 in exactly 0.012 kilogram of carbon-12, which is the Avogadro number of entities (approximately 6.023 x 10+23 entities).

Electric Current

The SI unit of electric current is the ampere, a fundamental unit of the SI. Since 1948, the ampere is by definition that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force exactly equal to 2 x 10-7 newton per metre of length. There are no other modern units in which current is measured, so no conversion factors are required.


Copyright 1997 James R. Fromm