﻿ Using Numbers and Unit Symbols in Measurements

## Using Numbers and Unit Symbols in Measurements

Every measurement includes two parts: a numerical value and a unit of measurement. The name of the unit of measurement can be given in full (2 kilograms, 6 feet) but often a symbol is used as an abbreviation (2 kg, 6 ft).

Numerical values

Decimal Points and Markers: In English-speaking countries (except South Africa), in Mexico and in most Asian countries the period (.) is used as the decimal marker (decimal point) to separate the whole number and fractional portions of a number. In continental Europe and most South American countries the decimal marker is the comma (,). The International System (SI) allows either the period or the comma to be used; the Dictionary uses the period. Wikipedia's decimal separator article has a lists of countries using each marker.

Digit grouping: Since the comma is often used as a decimal marker, it should not be used to separate groups of digits. The SI recommends that numbers having many digits be represented as groups of three digits separated by narrow spaces, like this: 2 675 491. The Dictionary observes this convention. The SI also allows large numbers to be written without any grouping, as in 2675491, but it does not allow the use of commas or any other grouping marks other than narrow spaces.

Large numbers: How many is a billion? In America, the word "billion" means the number 1 000 000 000, or 109. In Britain, this number is (or was) traditionally called "one milliard" or "one thousand million," and "billion" means the number 1 000 000 000 000 or 1012, which is what Americans call a "trillion." Most other European languages have similar expressions, such as mil millones for 109 and billón for 1012 in Spanish.

The Dictionary uses the American definitions for large number names. Although the General Conference on Weights and Measures endorsed the European names in 1948, the American definitions seem to be gaining ground in Britain and perhaps elsewhere. See Names for Large Numbers for more on this question.

There's always interest, especially among school children, in knowing the names of still larger numbers: quadrillions, quintillions, etc. These names are also listed in on the Names for Large Numbers page.

Using symbols in the International System (SI)

In the International System of Units (SI), the units do not have "abbreviations". They have symbols. The unit symbols do not follow the grammatical rules for abbreviations, because they follow the mathematical rules for symbols instead. These rules include the following.

• A symbol is never followed by a period (unless, of course, it happens to fall at the end of a sentence).
• The letter "s" is never added to a symbol to indicate a plural.
• In other words, 2 minutes is written 2 min, not 2 min. or 2 mins.
• Symbols are case-sensitive and must be written as they are defined.
• There is a tradition in the metric system that the first (or only) letter of an unprefixed unit symbol is capitalized if (and only if) the unit's name comes from a proper name. Thus W is the symbol for the watt and A is the symbol for the ampere, because these units are named for scientists.
• It makes a big difference whether a symbol is capitalized or not, because often the same letter represents different units: t stands for the tonne and T for the tesla, for example.
• There is one loophole in the rule on capitalization: it's acceptable to use the symbol L instead of l for the liter, since the letter l is so easily confused with the number 1.
• The case of symbol prefixes is specified, upper and lower, and must not be changed. For example, the symbol for kilo- is k-, so kW and not KW is the symbol for the kilowatt.
• The superscripts 2 and 3 are always used for "square" and "cubic", respectively.
• Thus the square kilometer, for example, is written km2, not sq km.
• A raised dot (also called a middle dot or half-high dot) is recommended when symbols are multiplied. It is permissible to use a space instead, but symbols should not be placed next to one another with nothing between them.
• For example, A·h is the recommended symbol for the ampere hour. A h is also permitted, but not Ah or amp hr.
• The slash (solidus) / is used for "per". Furthermore, only one slash is allowed per symbol.
• This means the SI unit of acceleration is written m/s2 rather than m/s/s, even though it is often spoken "meters per second per second". (Negative exponents can also be used: m/s2 can be written m·s-2.)
• Symbols are separated from the numerical quantity they follow by a space.
• Thus 5 kilograms is written 5 kg, not 5kg.

Using symbols for English customary units

In the English customary systems there are no "official" symbols or abbreviations. For many English units a variety of abbreviations are used. Sometimes these abbreviations duplicate metric symbols; for example, "A" is sometimes used in English for the acre instead of the ampere. It would be better to use the symbol "ac" for the acre. In this dictionary, the first symbol listed is either the official one or the one that should be preferred in order to minimize confusion of units.

The policy of this dictionary is to define symbols for the traditional English units and to apply the SI rules to their use. This is done for both consistency and clarity. It avoids a number of outstanding problems caused by the traditional abbreviations for the English units, especially the following.

• In the English systems, there is no general agreement as to whether abbreviations for units are capitalized or not. When English-speaking writers extend this informal practice to metric symbols, they sometimes create wild errors, such as "10 ML" used for 10 milliliters when it actually means 10 megaliters. Even standard dictionaries in English sometimes give the wrong case for metric symbols! In this dictionary, the SI convention for capitalization is applied (with a very few exceptions) to the symbols used for the English units: a letter is capitalized only if it comes from a proper name. Thus we write Btu (not BTU) for the British thermal unit.
• In English traditional unit abbreviations, the letter "p" is often used as an abbreviation for "per", "sq" or "s" as an abbreviation for "square", and "cu" or "c" as an abbreviation for "cubic". These are all bad ideas, despite their long usage, and they lead to confusing abbreviations.

If there is anything radical in this dictionary, here it is: applying SI rules to the symbols for English units means writing mi/hr instead of MPH, mi/gal instead of MPG, lb/in2 instead of PSI, and ft3/min instead of CFM. There's a small loss of space in doing this but a great gain in clarity.