Prefixes

Additional information about prefixes

 

Large numbers are unwieldy – difficult to calculate with, difficult to remember. Before the introduction of prefixes, one measurement unit per physical quantity was not enough. To avoid very large or very small numbers, several units for measuring the same thing were needed. That explains why there was such a multitude of units for measuring the same physical quantity, for example length, before the metric system was created.

Prefixes are a genial way of reducing the number of units needed – they introduce simplicity. As an example, a measurement system with prefixes might have ten units and ten prefixes, which leaves only twenty names and meanings to remember. To cover the same quantities and magnitudes without prefixes, a full one hundred units would be required.

 

 

Please note that more about the rules and conventions of using prefixes can be found on the page of rules.

Go to:

Systematic structure of the prefixes

The original prefixes: kilo, hecto, deca, deci, centi and milli

Binary prefixes

Encyclopaedia and history of prefixes

Obsolete prefixes and other names for prefixes

Names for large numbers – English

Names for large numbers – other languages

 

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Systematic structure of the prefixes

Most prefixes are multiples or sub-multiples of 1 000. That means that moving up or down one prefix moves the decimal marker by three digits. As a result, the exponent (when using the scientific notation with powers of ten, such as 10⁶) increases or decreases in multiples of three.

This system works very well with the custom of separating the digits of large numbers into groups of three (such as 1 234 567 890). When changing prefixes for a quantity value written in this style, the decimal marker simply jumps from one group of three digits to another group of three digits. Nothing could be easier, and it can all be done by mental arithmetic, without any conversion factors.

Other convenient rules to remember:

§           Symbols of prefixes that make a number larger consist of a capital letter

§           Symbols of prefixes that make a number smaller consist of a lower case letter

§           Names of prefixes that make a number larger end in ‘-a’

§           Names of prefixes that make a number smaller end in ‘-o’

More about rules and conventions can be found on the page of rules.

However, six prefixes, including the most commonly used prefixes ‘kilo’ and ‘milli’, do not conform to this scheme. For historic reasons, these prefixes are exceptions to the format of the newer prefixes.

 

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The original prefixes: kilo, hecto, deca, deci, centi and milli

 

 

The first and oldest prefixes

When the new metric system was first made legal on 1 August 1793, six prefixes were included:

§         kilo [k] for 1000, hecto [h] for 100, deca [da] for 10

§         deci [d] for 0.1, centi [c] for 0.01, milli [m] for 0.001

In 1960, when the set of prefixes was officially defined for use with the modern metric system by the 11^th CGPM, these prefixes were kept without changes.

As a result, all of them are exceptions to the rules. All of them have small letters as symbols, ‘deca’ is the only prefix that has two letters as symbol and the names ‘deca’ and ‘deci’ and their symbols are too similar for convenience.

However, they are officially part of the metric system. In terms of their legal or official status, they are not different from any other prefix.

Sometimes, the assumption is made that hecto, deca, deci and centi are not part of the SI or that they have been discontinued – this is not the case. All prefixes listed in the table of prefixes have the same status and can be equally applied.

Hecto, deca, deci and centi are usually avoided for scientific and technical use

 

 

Because there is little need for prefixes for 100, 10, 0.1 and 0.01, and because these old prefixes don’t fit well with the structure of the other prefixes, they are less and less used. In scientific and technical contexts, they are usually shunned. By custom, prefixes that are multiples or sub-multiples of 1000 are usually preferred.

However, this is only a convention that has established itself by practice, not a rule of the metric system. Centimeters etc. are thus perfectly acceptable, at least in areas where their use is already established.

The ISO permits the use of hecto, deca, deci and centi when other prefixes are inconvenient.

Usually, the four prefixes mentioned above are used in the context of centimeters, decibels, hectoliters and, to a lesser degree, centiliters. Some countries also use decagrams for cooking.

 

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Binary prefixes

All SI prefixes are decimal; they work with powers of ten. This corresponds with the prevailing decimal numbering system and makes understanding and changing prefixes trivial.

In computing, powers of two often occur naturally. As today’s microprocessors and memory banks can recognize only two states, on and off (o and 1), computers have to work with a binary numbering system.

Unfortunately, it is customary in the computing sector to express large numbers using decimal prefixes, when powers of two should be used. For example, one kilobyte in computing could mean 1 024 bytes (= 2¹⁰) instead of the 1 000 bytes (= 10³) that the prefix kilo would suggest.

 

The chaos and confusion is total. Some computer-related items, such as processor speed (in mega- or gigahertz) or the transfer rate of a communication line (in kilo-or megabytes per second) are measured decimally and metric prefixes are thus used correctly. Other items, such as the capacity of memory chips (in kilo- or megabytes) are measured in powers of two and metric prefixes are used wrongly.

It gets even worse when considering that correct and incorrect usage of metric prefixes can be mixed. One example is the 90 mm floppy disk, labelled with 1.44 megabyte capacity. The actual capacity is 1 474 560 bytes. The odd nominal label of 1.44 megabytes has been arrived at by mixing powers of ten and powers of two.

Manufacturers of hard disks usually measure disk capacity decimally and rightly use metric prefixes. Computer operating systems measure hard disk capacity in powers of two and incorrectly apply metric prefixes. Problems arise when the surprised user usually can’t understand why his brand new 250 gigabyte hard disk has only 233 gigabytes of space available according to his operating system.

 

To solve this problem, the BIPM has issued a clarification that metric prefixes must stand unambiguously for powers of ten while the IEC (International Electrotechnical Commission) has created a new set of binary prefixes. These prefixes are based on powers of two. Their names, symbols and the quantities they describe have been chosen to match the decimal metric prefixes as closely as possible.

 Table of binary prefixes

 

Although these prefixes have been published by the IEC in 1998 and the IEEE (Institute of Electrical and Electronics Engineers) accepted them in 2002, take-up has been slow.

The new prefixes are able to eliminate error and confusion. However, until their use becomes more widespread, the current muddle will continue. There is hardly an excuse for using decimal prefixes wrongly; it is an error.

 

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Encyclopaedia and history of prefixes

The table and dictionary of prefixes contains only current prefixes. Please check obsolete prefixes and other names for prefixes for names not in this list.

 

 

 

 

Yotta [Y] 10²⁴, one septillion; (from the Italian word otto, meaning eight). The initial letter and symbol ‘Y’ was chosen because it does not conflict with other metric symbols – another reason was that ‘o’ from otto could have been confused with the digit zero. Yotta is similar to the prefix ‘yocto’, which has a small letter ‘y’ as initial letter and symbol. ‘Y’ thus stands for 10²⁴ and ‘y’ for 10⁻²⁴; a choice that is both convenient and easy to remember. The number eight was chosen to indicate that this prefix stands for 10²⁴ = 10^3×8 = 1 000⁸. Yotta was adopted by the 19^th CGPM in 1991.

Zetta [Z] 10²¹, one sextillion; (from the Italian word sette, meaning seven). The initial letter ‘Z’ was chosen because it does not conflict with other metric symbols. It is similar to the prefix ‘zepto’, which has a small letter ‘z’ as initial letter and symbol. ‘Z’ thus stands for 10²¹ and ‘z’ for 10⁻²¹; a choice that is both convenient and easy to remember. The number seven was chosen to indicate that this prefix stands for 10²¹ = 10^3×7 = 1 000⁷. Zetta was adopted by the 19^th CGPM in 1991.

Exa [E] 10¹⁸, one quintillion; (from the Greek word hexa, meaning six). The first letter of hexa was dropped to create a new, unambiguous prefix for the metric system that can’t be confused with the Greek prefix used in words such as ‘hexagon’.  The number six was chosen to indicate that this prefix stands for 10¹⁸ = 10^3×6 = 1 000⁶. Exa was adopted by the 15^th CGPM in 1975.

Peta [P] 10¹⁵, one quadrillion; (from the Greek word penta, meaning five). Apparently, the third letter in the Greek word penta was dropped, because the same had been done to create the prefix “tera”. The reason behind this modification of penta was to create a new, unambiguous prefix for the metric system that can’t be confused with the Greek prefix used in words such as ‘pentagon’. The number five was chosen to indicate that this prefix stands for 10¹⁵ = 10^3×5 = 1 000⁵. Peta was adopted by the 15^th CGPM in 1975.

Tera [T] 10¹², one trillion; (from the Greek word teras, meaning monster). The Greek word tetras means four, but the third letter was dropped, giving us ‘tera’. This modification of tetras was done to create a new, unambiguous prefix for the metric system that can’t be confused with the Greek prefix used in words such as ‘tetragon’. The number four was chosen to indicate that this prefix stands for 10¹² = 10^3×4 = 1 000⁴. Tera was adopted by the 11^th CGPM in 1960.

Giga [G] 10⁹, one billion; (from the Greek word gigas, meaning giant). Giga was adopted by the 11^th CGPM in 1960.

Mega [M] 10⁶, one million; (from the Greek word megas, meaning large). This prefix was introduced by the BA (British Association for the Advancement of Science) as part of the CGS-system of units in 1874 when the new units for electricity and magnetism were standardized. At that time, the range of existing prefixes became too limited for science. Mega was officially adopted by the 11^th CGPM in 1960 when the SI system was established.

Kilo [k] 10³, one thousand; (from the Greek word khilioi, meaning thousand). This prefix was one of the original six prefixes of the metric system, when it became official on 1 August 1793. The idea at that time was to use Greek words for all prefixes that make a number larger, and Latin words for all prefixes that make a number smaller. The word kilo is a French adoption of the original Greek. Kilo was officially adopted by the 11^th CGPM in 1960 when the SI system was established. At that time, it was decided to keep all six original prefixes from 1793.

Please note that the symbol ‘k’ for kilo is set in lower case – in contrast to most other prefixes that make a number larger. This is because ‘k’ was already established before the rule of using capital letters for symbols of prefixes that make a number larger and lower case letters for prefixes that make a number smaller was introduced.

Hecto [h] 10², one hundred; (from the Greek word hekaton, meaning hundred). This prefix was one of the original six prefixes of the metric system, when it became official on 1 August 1793. The idea at that time was to use Greek words for all prefixes that make a number larger, and Latin words for all prefixes that make a number smaller. The word hecto is a French adoption of the original Greek. In contrast to most other prefixes, hecto is not a multiple or sub-multiple of 1 000, which is why it gets little use today. Hecto was officially adopted by the 11^th CGPM in 1960 when the SI system was established. At that time, it was decided to keep all six original prefixes from 1793.

Please note that the symbol ‘h’ for hecto is set in lower case – in contrast to most other prefixes that make a number larger. This is because ‘h’ was already established before the rule of using capital letters for symbols of prefixes that make a number larger and lower case letters for prefixes that make a number smaller was introduced.

Deca [da] 10¹, ten; (from the Greek word deka, meaning ten). This prefix was one of the original six prefixes of the metric system, when it became official on 1 August 1793. The idea at that time was to use Greek words for all prefixes that make a number larger, and Latin words for all prefixes that make a number smaller. The word deca is a French adoption of the original Greek. In contrast to most other prefixes, deca is not a multiple or sub-multiple of 1 000, which is why it gets little use today. In US English, ‘deca’ is usually spelled ‘deka’ (see also the conventions on spelling on the page about rules). Deca was officially adopted by the 11^th CGPM in 1960 when the SI system was established. At that time, it was decided to keep all six original prefixes from 1793.

Please note that the symbol ‘da’ for deca is set in lower case – in contrast to most other prefixes that make a number larger. This is because ‘da’ was already established before the rule of using capital letters for symbols of prefixes that make a number larger and lower case letters for prefixes that make a number smaller was introduced. The symbol for deca is also the only prefix symbol that consists of two letters.

‘Deca’ and ‘da’ are easily confused with ‘deci’ and ‘d’. Many people are unfamiliar with both prefixes, since they are hardly ever used. It is probably best to avoid using them.

 

 

This part is still under construction.

 

Deci [d] 10^-1, one tenth; (from the Latin word decimus, meaning tenth) F

Centi [c] 10^-2, one hundredth; (from the Latin word centum, meaning hundred) F

Milli [m] 10^-3, one thousandth; (from the Latin word mille, meaning thousand) F

Micro [µ] 10^-6, one millionth; (from the Greek word mikros, meaning small). This prefix was introduced by the BA (British Association for the Advancement of Science) as part of the CGS-system of units in 1874 when the new units for electricity and magnetism were standardized. At that time, the range of existing prefixes became too limited for science. Micro was officially adopted by the 11^th CGPM in 1960 when the SI system was established.

Before the abolishment by the 13^th CGPM in 1968, the name ‘micron’ was used as a measurement unit for length. The micron (symbol ‘µ’) stood for 0.000 001 meter. ‘Micron’ is now obsolete and has been replaced the micrometer (symbol ‘µm’), which is of identical length.

Nano [n] 10^-9, one billionth; (from the Greek word nanos, meaning dwarf).

Pico [p] 10^-12, one trillionth; (from the Spanish word pico, meaning small amount).

Femto [f] 10^-15, one quadrillionth; (from the Danish-Norwegian word femten, meaning fifteen).

This prefix was chosen because a unit for a very small distance, used in nuclear physics, had been called ‘fermi’ (symbol f or fm). This unit had been established before prefixes for very small quantities were defined.

The fermi was defined to be 10⁻¹⁵ m long. By adopting the name ‘femto’ and symbol ‘f’ for the prefix for 10⁻¹⁵, the new SI-consistent femtometer [fm] would equal one fermi. Thus replaced by the femtometer, fermi passed into obsolescence (see under obsolete units).

 

Atto [a] 10^-18, one quintillionth; (from the Danish-Norwegian word atten, meaning eighteen).

Zepto [z] 10^-21, one sextillionth; (from the Latin word septo, meaning seven).

Yocto [y] 10^-24, one septillionth (from the Latin word octo/the Greek word okto, meaning eight).

 

 

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Obsolete prefixes, compound prefixes and other names for prefixes

Obsolete prefixes

Only two prefixes were ever cancelled:

§         Myria [ma] or [my] = 10⁴ = 10 000

§         Myrio [mo] = 10⁻⁴ = 0.000 1

Both prefixes were made part of the metric system by a French law that came into effect on 1795-04-07. The origins of the word come from the Greek words myrioi, meaning ten thousand, and myrios, meaning countless.

In 1960, the metric system was overhauled by the 11^th CGPM and the name SI given to this most modern definition of metric weights and measures. Part of this process was the formal definition of prefixes. It was then decided to name only powers of 1 000. In addition, all the other original prefixes of 1793 (hecto, deca, deci and centi) were kept. Myria and myrio were not retained and became obsolete.

Compound prefixes

The original prefixes of the metric system covered a range from 0.001 to 1 000.  To create larger or smaller numbers, it was allowed to combine prefixes. For example, a millimillimeter would have been one thousandth of one thousandth of a meter (= micrometer).

Decimilli (0.1 mm) and centimilli (0.01 mm) were legal prefixes in France. When the table of prefixes was officially defined and extended by the 11^th CGPM in 1960, this practice was abolished.

Other names for prefixes

Sometimes other names for prefixes, (such as bronto, dea, ento, fito, hepa, otta, revo, syto, tredo, una, vendeka, vendeko, weka, weko, xenna, xenno) can be found. None of these are official; most of them appear to have been created for an Internet hoax.

 

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Names for large numbers – English

 

 

The English names for large numbers are listed in the table above.

The names are coined from the Latin words for small numbers. They were used first in the 15^th century in France and have since entered the vocabulary of all European languages.

However, the same words can describe numbers of different magnitude in different languages. For example, billion means 10⁹ in English, but 10¹² in German and French. The names for large numbers in most European languages are identical to the names in the traditional (now obsolete) British English usage.

The British usage of names for large numbers used to differ from the US usage. However, Britain adopted the US custom of naming large numbers in the 1970s. Therefore, all versions of English today use the same names for large numbers. However, the meanings of English names for large numbers in older documents can differ from today’s meanings.

 

To avoid confusion, the names for large numbers should be avoided in an international context. For many contexts, the metric prefixes can be used instead – they are unambiguous.

Please see also “Names for large numbers – other languages”.

 

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Names for large numbers – other languages