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SI Derived Unit
The International System of Units (SI) specifies a set of seven base units from which all other SI units of measurement are derived. These SI DERIVED UNITS are either dimensionless , or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation . Many derived units do not have special names. For example, the SI derived unit of area is the square metre (m2) and the SI derived unit of density is the kilogram per cubic metre (kg/m3 or kg m−3). However, 22 derived units are recognized by the SI with special names, which are written in lowercase. However, the symbols for units named after persons, are always written with an uppercase initial letter. For example, the symbol for the hertz is "Hz"; but the symbol for the metre is "m"
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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
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SI Base Unit
The International System of Units
International System of Units
(SI) defines seven units of measure as a basic set from which all other SI units can be derived . The SI BASE UNITS and their physical quantities are the metre for measurement of length , the kilogram for mass , the second for time , the ampere for electric current , the kelvin for temperature , the candela for luminous intensity , and the mole for amount of substance . The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with an initial capital letter
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Units Of Measurement
A UNIT OF MEASUREMENT is a definite magnitude of a quantity , defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of that quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity . The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre". The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common. Now there is a global standard, the International System of Units
International System of Units
(SI), the modern form of the metric system . In trade, WEIGHTS AND MEASURES is often a subject of governmental regulation, to ensure fairness and transparency
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Dimensionless Quantity
In dimensional analysis , a DIMENSIONLESS QUANTITY is a quantity to which no physical dimension is applicable. It is also known as a BARE NUMBER or a QUANTITY OF DIMENSION ONE. Dimensionless quantities are widely used in many fields, such as mathematics , physics , engineering , and economics . By contrast, examples of quantities with dimensions are length , time , and speed , which are measured in dimensional units, such as metre , second and metre per second
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Power (mathematics)
EXPONENTIATION is a mathematical operation , written as BN, involving two numbers, the BASE b and the EXPONENT n. When n is a positive integer , exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: b n = b b n {displaystyle b^{n}=underbrace {btimes cdots times b} _{n}} The exponent is usually shown as a superscript to the right of the base. In that case, bn is called b raised to the n-th power, b raised to the power of n, or the n-th power of b. When n is a positive integer and b is not zero, b−n is naturally defined as 1/bn, preserving the property bn × bm = bn + m. With exponent −1, b−1 is equal to 1/b, and is the reciprocal of b. The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices
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Square Metre
The SQUARE METRE (International spelling as used by the International Bureau of Weights and Measures ) or SQUARE METER (American spelling ) is the SI derived unit
SI derived unit
of area , with symbol m2 (33A1 in Unicode
Unicode
). It is the area of a square whose sides measure exactly one metre . The square metre is derived from the SI base unit
SI base unit
of the metre, which itself is defined as the length of the path travelled by light in absolute vacuum during a time interval of 1/299,792,458 of a second . Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is squared, the order of magnitude difference between units doubles from their comparable linear units. For example, a kilometre is 1000 times the length of a metre, but a square kilometre is 1,000,000 times the area of a square metre
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Density
The DENSITY, or more precisely, the VOLUMETRIC MASS DENSITY, of a substance is its mass per unit volume . The symbol most often used for density is _ρ_ (the lower case Greek letter rho ), although the Latin letter _D_ can also be used. Mathematically, density is defined as mass divided by volume: = m V , {displaystyle rho ={frac {m}{V}},} where _ρ_ is the density, _m_ is the mass, and _V_ is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume , although this is scientifically inaccurate – this quantity is more specifically called specific weight . For a pure substance the density has the same numerical value as its mass concentration . Different materials usually have different densities, and density may be relevant to buoyancy , purity and packaging
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Kilogram Per Cubic Metre
KILOGRAM PER CUBIC METRE is an SI derived unit
SI derived unit
of density , defined by mass in kilograms divided by volume in cubic metres . The official SI symbolic abbreviation is kg·m−3, or equivalently either kg/m3 or kg m 3 {displaystyle {tfrac {text{kg}}{{text{m}}^{3}}}!} . CONTENTS * 1 Conversions * 2 Relation to other measures * 3 See also * 4 References * 5 External links CONVERSIONS1 kg/m3 is equivalent to: = 0.001 g/cm3 (exactly) ≈ 0.06243 lb/ft3 (approximately) ≈ 0.1335 oz/gal (approximately) 1 g/cm3 = 1000 kg/m3 = 1,000,000 g/m3 (exactly) 1 lb/ft3 ≈ 16.02 kg/m3 (approximately) 1 oz/gal ≈ 7.489 kg/m3 (approximately) RELATION TO OTHER MEASURESThe kilogram was originally based on the mass of one litre of water, thus the density of water is about 1000 kg/m3 or 1 g/cm3. In chemistry , g/cm3 is more commonly used
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Hertz
The HERTZ (symbol: Hz) is the derived unit of frequency in the International System of Units
International System of Units
(SI) and is defined as one cycle per second . It is named for Heinrich Rudolf Hertz
Hertz
, the first person to provide conclusive proof of the existence of electromagnetic waves . Hertz
Hertz
are commonly expressed in multiples : kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), and terahertz (1012 Hz, THz). Some of the unit's most common uses are in the description of sine waves and musical tones , particularly those used in radio - and audio-related applications. It is also used to describe the speeds at which computers and other electronics are driven
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Metre
The METRE (international spelling ) or METER (American spelling ) (from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is M. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 seconds . The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole
North Pole
. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86 . In 1983, the current definition was adopted. The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about  3 3⁄8 inches longer than a yard , i.e. about  39 3⁄8 inches
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Radian
The RADIAN is the standard unit of angular measure, used in many areas of mathematics . The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at  A072097 ). The unit was formerly an SI supplementary unit , but this category was abolished in 1995 and the radian is now considered an SI derived unit . Separately, the SI unit of solid angle measurement is the steradian . The radian is represented by the symbol RAD. An alternative symbol is c, the superscript letter c, for "circular measure", or the letter r, but both of those symbols are infrequently used as it can be easily mistaken for a degree symbol (°) or a radius (r). So for example, a value of 1.2 radians could be written as 1.2 rad, 1.2 r, 1.2rad, or 1.2c
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Steradian
The STERADIAN (symbol: sr) or SQUARE RADIAN is the SI unit of solid angle . It is used in three-dimensional geometry, and is analogous to the radian which quantifies planar angles . The name is derived from the Greek stereos for "solid" and the Latin radius for "ray, beam". The steradian, like the radian, is a dimensionless unit, essentially because a solid angle is the ratio between the area subtended and the square of its distance from the vertex: both the numerator and denominator of this ratio have dimension length squared (i.e. L2/L2 = 1, dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W·sr−1). The steradian was formerly an SI supplementary unit , but this category was abolished in 1995 and the steradian is now considered an SI derived unit
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Si
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
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Symbol
A SYMBOL is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs. For example, a red octagon may be a symbol for "STOP". On a map, a blue line might represent a river. Numerals are symbols for numbers . Alphabetic letters may be symbols for sounds. Personal names are symbols representing individuals. A red rose may symbolize love and compassion. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space
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Physical Quantity
A PHYSICAL QUANTITY is a physical property of a phenomenon , body, or substance, that can be quantified by measurement . A physical quantity can be expressed as the combination of a magnitude expressed by a number – usually a real number – and a unit ; for example, 6973167492749999999♠1.6749275×10−27 kg (the mass of the neutron ), or 7008299792458000000♠299792458 metres per second (the speed of light ). Physical quantities are measured as n u {textstyle nu} _ where n {textstyle n} is the magnitude and u {textstyle u} is the unit. For example: A boy has measured the length of a room as 3 m. Here 3 is magnitude and m (metre) is the unit. 3 m can also be written as 300 cm. The same physical quantity x {textstyle x} can be represented equivalently in many unit systems, i.e._ x = n 1 u 1 = n 2 u 2 {textstyle x=n_{1}u_{1}=n_{2}u_{2}}
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