OpenMath Content Dictionary: units_siprefix1

Canonical URL:

http://www.openmath.org/cd/units_binaryprefix1.ocd

CD File:

units_siprefix1.ocd

CD as XML Encoded OpenMath:

units_siprefix1.omcd

Defines:

atto, centi, deci, deka, exa, femto, giga, hecto, kilo, mega, micro, milli, nano, peta, pico, tera, yocto, yotta, zepto, zetta

Date:

2004-08-27

Version:

1

Review Date:

2006-08-27

Status:

experimental

This CD defines symbols for the SI prefixes to indicate multiplication by a power of 10.

yotta

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^24$

Commented Mathematical property (CMP):

This is unit multiplication by $10^24$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="yotta" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 24 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (yotta, unit) ) , times (power ( 10 , 24 ) , unit) )

$$1\mathrm{prefix}(\mathrm{yotta},\mathrm{unit})={10}^{24}\mathrm{unit}$$

Signatures:

sts

zetta

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^21$

Commented Mathematical property (CMP):

This is unit multiplication by $10^21$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="zetta" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 21 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (zetta, unit) ) , times (power ( 10 , 21 ) , unit) )

$$1\mathrm{prefix}(\mathrm{zetta},\mathrm{unit})={10}^{21}\mathrm{unit}$$

Signatures:

sts

exa

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^18$

Commented Mathematical property (CMP):

This is unit multiplication by $10^18$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="exa" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 18 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (exa, unit) ) , times (power ( 10 , 18 ) , unit) )

$$1\mathrm{prefix}(\mathrm{exa},\mathrm{unit})={10}^{18}\mathrm{unit}$$

Signatures:

sts

peta

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^15$

Commented Mathematical property (CMP):

This is unit multiplication by $10^15$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="peta" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 15 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (peta, unit) ) , times (power ( 10 , 15 ) , unit) )

$$1\mathrm{prefix}(\mathrm{peta},\mathrm{unit})={10}^{15}\mathrm{unit}$$

Signatures:

sts

tera

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^12$

Commented Mathematical property (CMP):

This is unit multiplication by $10^12$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="tera" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 12 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (tera, unit) ) , times (power ( 10 , 12 ) , unit) )

$$1\mathrm{prefix}(\mathrm{tera},\mathrm{unit})={10}^{12}\mathrm{unit}$$

Signatures:

sts

giga

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^9$

Commented Mathematical property (CMP):

This is unit multiplication by $10^9$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="giga" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 9 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (giga, unit) ) , times (power ( 10 , 9 ) , unit) )

$$1\mathrm{prefix}(\mathrm{giga},\mathrm{unit})={10}^9\mathrm{unit}$$

Signatures:

sts

mega

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^6$

Commented Mathematical property (CMP):

This is unit multiplication by $10^6$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="mega" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 6 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (mega, unit) ) , times (power ( 10 , 6 ) , unit) )

$$1\mathrm{prefix}(\mathrm{mega},\mathrm{unit})={10}^6\mathrm{unit}$$

Signatures:

sts

kilo

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $1000$

Commented Mathematical property (CMP):

This is unit multiplication by $1000$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="kilo" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 3 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (kilo, unit) ) , times (power ( 10 , 3 ) , unit) )

$$1\mathrm{prefix}(\mathrm{kilo},\mathrm{unit})={10}^3\mathrm{unit}$$

Signatures:

sts

hecto

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $100$

Commented Mathematical property (CMP):

This is unit multiplication by $100$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="hecto" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 2 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (hecto, unit) ) , times (power ( 10 , 2 ) , unit) )

$$1\mathrm{prefix}(\mathrm{hecto},\mathrm{unit})={10}^2\mathrm{unit}$$

Signatures:

sts

deka

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10$

Commented Mathematical property (CMP):

This is unit multiplication by $10$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="deka" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> 1 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (deka, unit) ) , times (power ( 10 , 1 ) , unit) )

$$1\mathrm{prefix}(\mathrm{deka},\mathrm{unit})={10}^1\mathrm{unit}$$

Signatures:

sts

deci

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $0.1$

Commented Mathematical property (CMP):

This is unit multiplication by $0.1$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="deci" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -1 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (deci, unit) ) , times (power ( 10 , -1 ) , unit) )

$$1\mathrm{prefix}(\mathrm{deci},\mathrm{unit})={10}^{-1}\mathrm{unit}$$

Signatures:

sts

centi

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $0.01$

Commented Mathematical property (CMP):

This is unit multiplication by $0.01$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="centi" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -2 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (centi, unit) ) , times (power ( 10 , -2 ) , unit) )

$$1\mathrm{prefix}(\mathrm{centi},\mathrm{unit})={10}^{-2}\mathrm{unit}$$

Signatures:

sts

milli

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $0.001$

Commented Mathematical property (CMP):

This is unit multiplication by $0.001$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="milli" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -3 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (milli, unit) ) , times (power ( 10 , -3 ) , unit) )

$$1\mathrm{prefix}(\mathrm{milli},\mathrm{unit})={10}^{-3}\mathrm{unit}$$

Signatures:

sts

micro

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-6$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-6$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="micro" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -6 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (micro, unit) ) , times (power ( 10 , -6 ) , unit) )

$$1\mathrm{prefix}(\mathrm{micro},\mathrm{unit})={10}^{-6}\mathrm{unit}$$

Signatures:

sts

nano

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-9$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-9$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="nano" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -9 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (nano, unit) ) , times (power ( 10 , -9 ) , unit) )

$$1\mathrm{prefix}(\mathrm{nano},\mathrm{unit})={10}^{-9}\mathrm{unit}$$

Signatures:

sts

pico

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-12$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-12$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="pico" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -12 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (pico, unit) ) , times (power ( 10 , -12 ) , unit) )

$$1\mathrm{prefix}(\mathrm{pico},\mathrm{unit})={10}^{-12}\mathrm{unit}$$

Signatures:

sts

femto

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-15$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-15$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="femto" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -15 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (femto, unit) ) , times (power ( 10 , -15 ) , unit) )

$$1\mathrm{prefix}(\mathrm{femto},\mathrm{unit})={10}^{-15}\mathrm{unit}$$

Signatures:

sts

atto

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-18$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-18$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="atto" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -18 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (atto, unit) ) , times (power ( 10 , -18 ) , unit) )

$$1\mathrm{prefix}(\mathrm{atto},\mathrm{unit})={10}^{-18}\mathrm{unit}$$

Signatures:

sts

zepto

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-21$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-21$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="zepto" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -21 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (zepto, unit) ) , times (power ( 10 , -21 ) , unit) )

$$1\mathrm{prefix}(\mathrm{zepto},\mathrm{unit})={10}^{-21}\mathrm{unit}$$

Signatures:

sts

yocto

Description:

This symbol represents the fact that the subsequent unit has been effectively multiplied by $10^-24$

Commented Mathematical property (CMP):

This is unit multiplication by $10^-24$

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMA>
      <OMS name="prefix" cd="units_ops1"/>
      <OMS name="yocto" cd="units_siprefix1"/>
      <OMV name="unit"/>
    </OMA>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMI> 10 </OMI>
      <OMI> -24 </OMI>
    </OMA>
    <OMV name="unit"/>
  </OMA>
</OMA>
</OMOBJ>

eq (times ( 1 , prefix (yocto, unit) ) , times (power ( 10 , -24 ) , unit) )

$$1\mathrm{prefix}(\mathrm{yocto},\mathrm{unit})={10}^{-24}\mathrm{unit}$$

Signatures:

sts