Mathematics
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Measurement
Measurement is a way of finding and describing the size, length or amount of something. There are units of measurement to describe length (how far something is from end to end); mass (the amount of matter present in something); capacity (the amount that something can contain), and hundreds of other quantities. There are two main systems of weights and measures: Imperial, and the International System of Units or Système Internationale (SI). Imperial was formerly used across the British Empire, including what became the United States, and includes inches, feet, ounces and pounds, along with other units. SI is based on the metric system, devised in France in the 18th century.
History
Early units of weights and measures used the human body and nature. Ancient Babylonian and Egyptian records from about 3000 BC show length was measured with the forearm, hand and finger. Grain could be used to measure capacity. Later, the Romans set standard measures including units such as the palm, feet and paces in a system of weights and measures. Miles, pounds and ounces, all devised by the Romans, are still in use today.
Measures were standardized in medieval England to make trade easier. When Britain became a powerful nation, its weights and measures were adopted worldwide as the British Imperial System. In the 1824 Weights and Measures Act, one standard system replaced the many variations that had appeared over the years.
The metric system
In 1800 France adopted the metric system, devised by the French Academy of Sciences. This defined a metre as a ten-millionth of the length of the meridian line that passed through Paris from the North Pole to the equator. Other units were set in similarly exact scientific terms. The simplicity of the metric system—all measures are divided or multiplied by 10—gained it popularity and it spread around the world, along with the growing international influence of France since the French Revolution. In 1983 the metre was redefined more precisely as the distance travelled by light in just under one three hundred millionths of a second. The system uses "kilo" to show 1000 units.
Système Internationale
The International System of Units, or Système Internationale (SI) is based on the metric system. A small number of base units, (which today includes units of mass, length, time and temperature and three others) are first defined, and then all other units (called derived units) are defined by using the base units.
The SI system is also a decimal system, in which each kind of unit is defined in multiples of 10. So there are 10 millimetres in a centimetre, 10 centimetres in a decimetre, 10 decimetres in a metre, and so on. SI is now the recognized system of measurement used all over the world.
A metric prefix indicate either a multiple or fraction of that unit. The prefix kilo-, for example, indicates multiplication by one thousand, while the prefix milli- indicates division by one thousand. A set of prefixes enables us to measure things ranging from the extremely large down to the extremely tiny. A gigalitre, for example, is 1 billion litres (1 followed by nine zeros). A nanometre is 1 billionth of a metre (nine places to the right of the decimal point).
Units of length
Imperial units of length are: the inch, 12 of which make a foot, 3 of which make a yard, 1760 of which make a mile. Using SI, a metre (equivalent to about 1.09 yards or 3.28 feet) can be broken down into 10 decimetres, 100 centimetres, 1000 millimetres and so on. One kilometre is 1000 metres.
Astronomical distances
Distances to the stars or galaxies are far too great to be given in kilometres, so, among several other units, the light year is sometimes used by astronomers. This is the distance light, which moves at a speed of about 300,000 kilometres per second, travels through a vacuum (such as space) in one year: about 9,460,730,500,000 kilometres (5,878,625,000,000 miles). The nearest star to Earth (after the Sun), Proxima Centauri, is 4.2 light years away.
For measuring distances within the Solar System or around other stars, astronomers use a unit of length called the astronomical unit (au or AU). It is the average distance from Earth to the Sun, approximately equal to 150 million kilometres (93 million miles) or 8.3 light-minutes. The actual distance varies by a small amount as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once each year. Since 2012, 1 AU has been defined as exactly 149,597,870.7 kilometres.
To measure the distances of stars less than about 1600 light years from Earth, astronomers use the parallax technique. We know Earth orbits the Sun at a distance of about 150 million kilometres (93 million miles). By recording the position of a star one day, and then again 6 months later, astronomers can observe the difference in the viewing angle for the star. Using basic geometry—the viewing angles and the distance of one side of the triangle (the diameter of Earth's orbit) are known—the star's distance can be calculated. This is also called triangulation.
Astronomers use a unit of length called the parsec (pc) to give the star's distance. The measurement is arrived at through the parallax method (the word parsec is short for "parallax of one second"), and is equal to 206,000 AU. This is roughly equal to 3.26 light years or 30.9 trillion kilometres.
The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun. The Pleiades, a star cluster in the constellation Taurus, lie at about 136 parsecs. Most stars visible to the naked eye are within a few hundred parsecs of the Sun, while the most distant stars lie at about 4 billion parsecs.
The parallax method is used to measure the distances of stars less than about 500 parsecs (approximately 1600 light years) from Earth. To measure the distance to stars up to about 10,000 parsecs from Earth, astronomers measure the star's magnitude (brightness), as indicated by its spectrum. By comparing this measure, the absolute magnitude (the star's actual brightness), with its apparent magnitude (its brightness as seen from Earth)—that is, how dim the light has become on reaching Earth—the star's distance can be calculated.
Mass
Mass is the amount of matter present in a body. Weight is how strongly gravity pulls on it. So an object sent into outer space will have the same mass as on Earth, but no weight, because there is no force of gravity pulling it down. However, for everyday purposes, mass is normally expressed as "weight".
In imperial measures, mass is described in ounces, 16 of which make a pounds, 14 of which make a stone. A ton is 2240 pounds, but in the USA it is 2000 pounds, so the first is described as a "long ton" and the second a "short ton". The SI base unit is the kilogram, and derived units include the gram (a thousandth of a kilogram) and tonnes (a thousand kilograms). By coincidence a tonne and a long ton are nearly equal (one long ton is 1.016 tonnes).
Capacity
Capacity and volume are very similar. Capacity is the maximum amount something can contain. Volume is how much three-dimensional space it occupies. In imperial measure, capacity is measured in fluid ounces, eight of which make a cup, while two cups make a pint and eight pints make a gallon.
In metric measures, capacity is often measured in litres. A litre is a volume equal to a cube measuring 10 centimetres on each side, that is, 1000 cubic centimetres. A millilitre (ml, often pronounced "mil") is a thousandth of a litre.
Extreme measures
Four new prefixes have been introduced in 2022 for extreme measures. At the tiniest end of the scale are ronto- (27 places to the right of the decimal point) and quecto- (30 places to the right of the decimal point, or a thousand times smaller). An electron, a subatomic particle, weighs about a rontogram.
At the top end of the scale are ronna- (one followed by 27 zeros) and quetta- (one followed by 30 zeros, or a thousand times bigger). The Earth can now be said to weigh six ronnagrams, Jupiter about two quettagrams.
Consultant: Mike Goldsmith