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Math Unit Conversions

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Mathematical quantities such as length, volume, mass etc. are expressed in certain standards of measurement. These measurement standards are known as units.
There are three types of unit systems under which units of mathematical quantities are measured. These unit systems are:

  • SI (International System of Units, Meter, Kilogram, Second) system
  • CGS (Centimeter Gram Second) system
  • FPS (Foot Pound Second) system
Standard units for length, mass and time are meter (m), kilogram (kg), and second (s) respectively. These units can be converted from one into another for a particular quantity.

This process is called conversion of units. One unit can be converted into another unit by the use of conversion factor. This conversion factor is a constant value. When we multiply or divide the conversion factor with a unit, then it will be converted into another unit. Unit conversion is possible only for the same quantity. In other words, a unit of length can be converted only into another unit of length.

Length Unit Conversion

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The standard unit of length is meter. It can be converted into other units. The list of length unit conversion factors is given below:
  • $1\ kilometer=1000\ meter$ or $1\ km=1000\ m$
  • $1\ hectometer=100\ meter$ or $1\ hm=100\ m$
  • $1\ decameter=10\ meter$ or $1\ dam=10\ m$
  • $1\ decimeter$ = $\frac{1}{10}$$\ meter$ or $1\ dm$ = $\frac{1}{10}$$\ meter$
  • $1\ centimeter$ = $\frac{1}{100}$$\ meter$ or $1\ cm$ = $\frac{1}{100}$$\ m$
  • $1\ millimeter$ = $\frac{1}{1000}$$\ meter$ or $1\ mm$ = $\frac{1}{1000}$$\ m$
  • $1\ cm=0.394\ inch$
  • $1\ foot=12\ inch$
  • $1\ inch=2.54\ cm$
  • $1\ foot=0.3048\ m$
  • $1\ yard=0.9144\ m$
  • $1\ mile=1.61\ km$
  • $1\ angstrom=10^{-10}\ meter$

Area Unit Conversion

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The standard unit of area is square meter which is abbreviated as sq m or m2. It can be converted into other units. The list of area unit conversion factors is given below:
  • $1\ km^{2}=10^{6}\ m^{2}$
  • $1\ hm^{2}=10^{4}\ m^{2}$
  • $1\ dam^{2}=10^{2}\ m^{2}$
  • $1\ dm^{2}=10^{-2}\ m^{2}$
  • $1\ cm^{2}=10^{-4}\ m^{2}$
  • $1\ mm^{2}=10^{-6}\ m^{2}$
  • $1\ hectare=10^{4}\ m^{2}$
  • $1\ square foot=0.092903\ m^{2}$

Volume Unit Conversion

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The standard unit of volume is cubic meter which is abbreviated as m3. Volume is expressed as liter also. Volume units can be converted into other units. The list of volume unit conversion factors is given below:
  • $1\ kiloliter=1000\ liter$ or $1\ kl=1000\ l$
  • $1\ hectoliter=100\ liter$ or $1\ hl=100\ l$
  • $1\ decaliter=10\ liter$ or $1\ dal=10\ l$
  • $1\ deciliter$ = $\frac{1}{1000}$$\ liter$ or $1\ dl$ = $\frac{1}{10}$$\ l$
  • $1\ centiliter$ = $\frac{1}{100}$$\ liter$ or $1\ cl$ = $\frac{1}{100}$$\ l$
  • $1\ milliliter$ = $\frac{1}{1000}$$\ liter$ or $1\ ml$ = $\frac{1}{1000}$$\ l$
  • $1\ gallon=3.78541\ liter$
  • $1\ liter=1000\ cubic\ centimeter$

Mass Unit Conversion

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The list of mass unit conversion is given below:
  • $1\ kilogram=1000\ gram$ or $1\ kg=1000\ g$
  • $1\ hectogram=100\ gram$ or $1\ hg=1000\ g$
  • $1\ decagram=10\ gram$ or $1\ dag=10\ g$
  • $1\ decigram$ = $\frac{1}{1000}$$\ gram$ or $1\ dg$ = $\frac{1}{10}$$\ g$
  • $1\ centigram$ = $\frac{1}{100}$$\ gram$ or $1\ cg$ = $\frac{1}{100}$$\ g$
  • $1\ milligram$ = $\frac{1}{1000}$$\ gram$ or $1\ mg$ = $\frac{1}{1000}$$\ g$
  • $1\ pound=453.592\ gram$
  • $1\ ounce=28.3495\ gram$
  • $1\ stone=6350.29\ gram$

Time Unit Conversion

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The standard unit of time is second which is abbreviated as "s". The list of time unit conversion factors is given below:
  • $1\ hour = 60\ minutes = 3600\ seconds$
  • $1\ minute = 60\ seconds$
  • $1\ millisecond = 10^{-3}\ seconds$
  • $1\ microsecond = 10^{-6}\ seconds$
  • $1\ nanosecond = 10^{-9}\ seconds$