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Metric Prefix
A METRIC PREFIX is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic , historically there have been a number of binary metric prefixes as well. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix _kilo- _, for example, may be added to _gram_ to indicate _multiplication_ by one thousand: one kilogram is equal to one thousand grams. The prefix _milli- _, likewise, may be added to _metre_ to indicate _division_ by one thousand; one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the metric system , with six dating back to the system's introduction in the 1790s. Metric prefixes have even been prepended to non-metric units. The SI PREFIXES are standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities
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Unit Prefix
A UNIT PREFIX is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes . The prefixes of the metric system , such as kilo and milli , represent multiplication by powers of ten. In information technology it is common to use binary prefixes , which are based on powers of two . Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations
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Multiple (mathematics)
In science , a MULTIPLE is the product of any quantity and an integer . In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n, which is called the multiplier . If a is not zero , this is equivalent to saying that b/a is an integer. In mathematics , when a and b are both integers, and b is a multiple of a, then a is called a divisor of b. One says also that a divides b. If a and b are not integers, mathematicians prefer generally to use INTEGER MULTIPLE instead of multiple, for clarification. In fact, multiple is used for other kinds of product; for example, a polynomial p is a multiple of another polynomial q if there exists third polynomial r such that p = qr. In some old texts, "a is a SUBMULTIPLE of b" was equivalent with "b is a multiple of a". This terminology is no more in use, except for units of measurement , where a submultiple of a main unit is a unit, named by prefixing the main unit, which is a quotient of the main unit by an integer, generally a power of 10. For example, a millimetre is a submultiple of a metre . CONTENTS * 1 Examples * 2 Properties * 3 References * 4 See also EXAMPLES14, 49, –21 and 0 are multiples of 7, whereas 3 and –6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0 and –21, while there are no such integers for 3 and –6
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Fraction (mathematics)
A FRACTION (from Latin
Latin
fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: 1 2 {displaystyle {tfrac {1}{2}}} and 17/3) consists of an integer numerator displayed above a line (or before a slash), and a non-zero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole. The picture to the right illustrates 3 4 {displaystyle {tfrac {3}{4}}} or ¾ of a cake. Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all of which are equivalent to 1/100). An integer such as the number 7 can be thought of as having an implicit denominator of one: 7 equals 7/1
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Decimal
The DECIMAL numeral system (also called BASE-TEN and occasionally called DENARY) has ten as its base , which, in decimal, is written 10, as is the base in every positional numeral system. It is the numerical base most widely used by modern civilizations. _ Decimal notation_ often refers to a base-10 positional notation such as the Hindu-Arabic numeral system ; however, it can also be used more generally to refer to non-positional systems such as Roman or Chinese numerals which are also based on powers of ten. A _decimal number_, or just _decimal_, refers to any number written in decimal notation , although it is more commonly used to refer to numbers that have a fractional part separated from the integer part with a decimal separator (e.g. 11.25). A decimal may be a terminating decimal, which has a finite fractional part (e.g. 15.600); a repeating decimal , which has an infinite (non-terminating) fractional part made up of a repeating sequence of digits (e.g. 5.123144 ); or an infinite decimal, which has a fractional part that neither terminates nor has an infinitely repeating pattern (e.g. 3.14159265...). Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, whereas irrational numbers have infinite non-repeating decimal representations
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Binary Number
In mathematics and digital electronics , a BINARY NUMBER is a number expressed in the BINARY NUMERAL SYSTEM or BASE-2 NUMERAL SYSTEM which represents numeric values using two different symbols: typically 0 (zero) and 1 (one) . The base -2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates , the binary system is used internally by almost all modern computers and computer-based devices . Each digit is referred to as a bit
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Kilo-
KILO (from the Greek χίλιοι, literally a thousand) is a decimal unit prefix in the metric system denoting multiplication by one thousand (103). It has been used in the International System of Units where it has the unit symbol K, in lower case. The prefix kilo is derived from the Greek word χίλιοι (chilioi), meaning "thousand". It was originally adopted by Antoine Lavoisier 's research group in 1795, and introduced into the metric system in France with its establishment in 1799. In 19th century English it was sometimes spelled chilio, in line with a puristic opinion by Thomas Young CONTENTS * 1 Examples * 2 kilobyte * 3 Exponentiation * 4 See also * 5 References EXAMPLES * one kilogram is 1000 grams * one kilometre is 1000 metres * one kilojoule is 1000 joules * one kilobaud is 1000 baud * one kilohertz is 1000 hertz * one kilobit is 1000 bits * one kilobyte (kB) is 1000 bytes KILOBYTEFor the kilobyte, a second definition has been in common use in some fields of computer science and information technology, which is, however, inconsistent with the SI definition. It uses kilobyte to mean 210 bytes (= 1024 bytes), because of the mathematical coincidence that 210 is approximately 103. The reason for this application is that binary values natively used in computing are base 2 values, and not decimal
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Milli-
MILLI- (symbol M) is a unit prefix in the metric system denoting a factor of one thousandth (10−3). Proposed in 1793 and adopted in 1795, the prefix comes from the Latin mille, meaning "one thousand" (the Latin plural is milia). Since 1960, the prefix is part of the International System of Units (SI). Example: * Snow
Snow
is crystalline water and is about 1 millimetre in diameter
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Metric System
The METRIC SYSTEM is an internationally agreed decimal system of measurement . It was originally based on the _mètre des Archives _ and the _kilogramme des Archives _ introduced by the French First Republic in 1799, but over the years the definitions of the metre and the kilogram have been refined, and the metric system has been extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries, the term is now often used as a synonym for "SI" or the " International System of Units "—the official system of measurement in almost every country in the world. The metric system has been officially sanctioned for use in the United States since 1866, but the U.S. remains the only industrialised country that has not fully adopted the metric system as its official system of measurement, although, in 1988, the United States Congress passed the Omnibus Foreign Trade and Competitiveness Act , which designates "the metric system of measurement as the preferred system of weights and measures for U.S. trade and commerce". Among many other things, the act requires federal agencies to use metric measurements in nearly all of its activities, although there are still some exceptions allowing traditional linear units to be used in documents intended for consumers
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International System Of Units
The INTERNATIONAL SYSTEM OF UNITS (abbreviated as SI, from the French _Système internationale (d'unités)_) is the modern form of the metric system , and is the most widely used system of measurement . It comprises a coherent system of units of measurement built on seven base units . The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the centimetre–gram–second system (CGS). SI is intended to be an evolving system, so prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The 24th and 25th General Conferences on Weights and Measures (CGPM) in 2011 and 2014, for example, discussed a proposal to change the definition of the kilogram , linking it to an invariant of nature rather than to the mass of a material artefact, thereby ensuring long-term stability. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems and the lack of coordination between the various disciplines that used them
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International Bureau Of Weights And Measures
Coordinates : 48°49′45.55″N 2°13′12.64″E / 48.8293194°N 2.2201778°E / 48.8293194; 2.2201778 The INTERNATIONAL BUREAU OF WEIGHTS AND MEASURES (French : _BUREAU INTERNATIONAL DES POIDS ET MESURES_) is an international standards organisation , one of three such organisations established to maintain the International System of Units
International System of Units
(SI) under the terms of the Metre Convention (_Convention du Mètre_). The organisation is usually referred to by its French initialism , BIPM. The BIPM reports to the International Committee for Weights and Measures (French : _Comité international des poids et mesures, CIPM_), which is in turn overseen by periodic meetings of the General Conference on Weights and Measures (French : _Conférence générale des poids et mesures, CGPM_). These organizations are also commonly referred to by their French initialisms. CONTENTS * 1 History * 2 Function * 3 Directors of the BIPM * 4 See also * 5 References * 6 External links HISTORYThe BIPM was created on 20 May 1875, following the signing of the Metre Convention , a treaty among 51 nations (as of August 2008 )
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International System Of Quantities
The INTERNATIONAL SYSTEM OF QUANTITIES (ISQ) is a system based on seven base quantities : length , mass , time , electric current , thermodynamic temperature , amount of substance , and luminous intensity . Other quantities such as area , pressure , and electrical resistance are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units and also includes many other quantities in modern science and technology. The ISQ is defined in the international standard ISO/IEC 80000 , and was finalised in 2009 with the publication of ISO 80000-1 . The 14 parts of ISO/IEC 80000 define quantities used in scientific disciplines such as mechanics (e.g., pressure ), light, acoustics (e.g., sound pressure ), electromagnetism, information technology (e.g., storage capacity ), chemistry, mathematics (e.g., Fourier transform ), and physiology. CONTENTS * 1 Base quantities * 2 Derived quantities * 2.1 Dimensions of derived quantities * 2.2 Logarithmic quantities * 3 References * 4 Further reading BASE QUANTITIESA base quantity is a physical quantity in a subset of a given system of quantities that is chosen by convention, where no quantity in the set can be expressed in terms of the others. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics
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Si Prefix
A METRIC PREFIX is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic , historically there have been a number of binary metric prefixes as well. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix kilo- , for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli- , likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre. Decimal
Decimal
multiplicative prefixes have been a feature of all forms of the metric system , with six dating back to the system's introduction in the 1790s. Metric prefixes have even been prepended to non-metric units. The SI PREFIXES are standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities
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Short Scale
The LONG AND SHORT SCALES are two of several large-number naming systems for integer powers of ten that use the same words with different meanings: Long scale Every new term greater than million is one million times larger than the previous term. Thus, billion means a million millions (1012), trillion means a million billions (1018), and so on. Thus, an n-illion equals 106n. Short scale Every new term greater than million is one thousand times larger than the previous term. Thus, billion means a thousand millions (109), trillion means a thousand billions (1012), and so on. Thus, an n-illion equals 103n + 3. For whole numbers less than a thousand million (< 109) the two scales are identical. From a thousand million up (≥ 109) the two scales diverge, using the same words for different numbers; this can cause misunderstanding. Countries where the long scale is currently used include most countries in continental Europe
Europe
and most French-speaking , Spanish-speaking , and Portuguese-speaking countries except Brazil
Brazil
. The short scale is now used in most English-speaking and Arabic-speaking countries , in Brazil
Brazil
, in the former Soviet Union
Soviet Union
and several other countries. Number
Number
names are rendered in the language of the country, but are similar everywhere due to shared etymology (e.g., billion is billón in Spanish)
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Long Scale
The LONG AND SHORT SCALES are two of several large-number naming systems for integer powers of ten that use the same words with different meanings: Long scale Every new term greater than million is one million times larger than the previous term. Thus, billion means a million millions (1012), trillion means a million billions (1018), and so on. Thus, an n-illion equals 106n. Short scale Every new term greater than million is one thousand times larger than the previous term. Thus, billion means a thousand millions (109), trillion means a thousand billions (1012), and so on. Thus, an n-illion equals 103n + 3. For whole numbers less than a thousand million (< 109) the two scales are identical. From a thousand million up (≥ 109) the two scales diverge, using the same words for different numbers; this can cause misunderstanding. Countries where the long scale is currently used include most countries in continental Europe and most French-speaking , Spanish-speaking , and Portuguese-speaking countries except Brazil . The short scale is now used in most English-speaking and Arabic-speaking countries , in Brazil , in the former Soviet Union and several other countries. Number names are rendered in the language of the country, but are similar everywhere due to shared etymology (e.g., billion is billón in Spanish). Some languages, particularly in East Asia and South Asia , have large number naming systems that are different from both the long and short scales, for example the Indian numbering system
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Yotta-
YOTTA is the largest decimal unit prefix in the metric system , denoting a factor of 1024 or 1000000000000000000000000; that is, one million million million million, or one septillion. It has the unit symbol Y. The prefix name is derived from the Ancient Greek οκτώ (októ), meaning "eight", because it is equal to 1,0008. It was added as an SI prefix to the