International System of Units

Questions on this topic? Just ask!

International System of Units

Measurement is one of the hallmarks of civilization. How far is it? How much does it weigh? What time is it? These are all questions that we hear every day. Indeed, asking the time is probably the number one question that we ask, especially when we are doing something we don't like!

Simple units, such as the cubit, which is the distance between a man's elbow and the tip of his middle finger, or the span, the distance from the tip of the thumb to the tip of the little finger of an outstretched hand, were used for much of recorded history. After all, the human body is always available for measuring distance. But it does suffer from one inherent problem. Not all men are created equal! Some are taller than others so that not all forearms are the same length.

Of course, this led to disputes and difficulties. Solving such problems was probably the basis for the origin of civil law. How does one stop people from cheating by using a favorable measurement? The answer is to standardize the system of weights and measures. Records indicate that the Egyptians started this practice as early as 3000 B.C., probably as a result of the annual flooding of all of the arable land along the Nile. This necessitated accurate surveying every year and resulted in the early Egyptians developing an excellent understanding of geometry and surveying.

By the late eighteenth century, scientists and engineers were able to construct very precise measuring instruments but the standard units for measurement were poorly defined. To develop a systematic and precise set of measurement standards, a commission, including scientists Pierre-Simon Laplace, Joseph-Louis Lagrange, and Antoine-Laurent Lavoisier, was established. They developed a system based on objects or phenomena that could be measured reproducibly; these natural measurements were independent of man. For instance, the meter (Greek for "to measure"), the basic unit of length, was calculated to be 1/10,000,000 of the distance between the North Pole and the equator on a line running through Paris. Other units were worked out to interconnect with the meter. For example, the liter (a derived unit of volume) is the volume occupied by one cubic decimeter, while the kilogram (the basic unit of mass) is the mass of a liter of water at 4°C. Smaller and larger units were available by multiplying and dividing by powers of 10.

This so-called metric system was by far the most logical and scientifically based system of measurement devised. Metric units are related decimally (i.e., by powers of 10). There have been many meetings and conferences to establish exact interpretations for the metric system. The original meter was defined as the distance between two marks on a platinum/iridium bar kept in a locked, air-conditioned vault maintained by the International Bureau of Weights and Measures in Paris. In 1960, the General Conference of Weights and Measurements redefined the meter as 1,650,763.73 wavelengths of one of the spectroscopic lines of an isotope of the noble gas, krypton. In 1983, it was further refined to be 1/299,792,458 of the distance that light travels in a second.

The General Conference of Weights and Measurements in 1960 established a revised metric system as the "International System of Units." The French name is "Le Syst(me International d'Unités" or the "Système International," for short, and it is this latter term that leads to the abbreviation "SI." Scientists all over the world have agreed to SI units as the basis for measurement. Indeed, with the exception of the United States, all of the countries in the world use SI units for commerce as well. The SI system is also called MKSA (meter, kilogram, second, ampere). The seven base units of the SI system, each of which is used for a particular physical quantity, are shown in figure 1.

Modification of the units is accomplished decimally using the prefixes. For example, 5 teraseconds = 5 Ts = 5 x 1012 s, while 5 milliseconds = 5 ms = 5 x 10-3 s, and 5 femtoseconds = 5 fs = 5 x 10-15 s. While the base SI unit for weight is the kilogram (kg), for many purposes in chemistry the smaller weight unit, gram (g), is more convenient; 1 kg = 1,000 g.

All other physical quantities can be derived from appropriate combinations of the seven basic units. Examples of these derived units include: 1) The SI unit of force is defined as the newton (N) which is a kilogram times the acceleration in meters per second squared or N = kg m/s2 . 2) The SI unit of energy is the joule (J); this unit is defined as the amount of energy required to apply a newton of force over the distance of one meter or J = N m. 3) The unit of charge, the coulomb (C), is the amount of electricity in 1 ampere during 1 second of time (C = A s). 4) The SI unit of area is the square meter or m2 . 5) The SI unit of volume is the cubic meter or m3 . 6) The unit of density (d) is the kilogram per cubic meter or d = kg/m3 .

The United States has been reluctant to completely adopt the SI units and still favors older units in some cases. Traditional units for distance such as the mile (= 1.609 km) and the yard (= 0.9144 m) are commonly employed. Other commonly used non-SI units are the pound (= 0.45359 kg) for weight and the quart (= 0.9463 L = 0.9463 dm3 ) for volume. Moreover, there has not been complete adoption of the SI units in the scientific community and in some instances traditional metric units, called CGS units, continue to find use. This reluctance to change completely to SI units is likely mostly due to comfort and tradition. Nevertheless, the older units are slowly being supplanted by the SI system.

Constructing derived units is relatively straightforward in the SI system, which is, in part, the reason that scientists have adopted it. However, it also has one other distinct advantage over some older systems of measurements and that is scalability. A meter is the basic unit of length but shorter and longer units are obtained by multiplication by factors of 10. For example, a centimeter is 1/100 of a meter, while a kilometer is 1,000 meters in length. Similarly, a centigram is 1/100 of a gram, while a kilogram is 1,000 grams. This commonality of prefixes for shifting powers of 10 makes scientific measurement very much easier, particularly where scientists are investigating the very small and the very large. For example, the nucleus of an atom is about 1 fm or 1 x 10-15 m in diameter and our galaxy is about 10 exameters or 1 x 1019 m in diameter.