# Formula page

### APES SI Prefix Unit Conversion Revision Table (10⁹ → 10⁻⁹)

  
<div class="table" id="bkmrk-namescientific-notat"><div id="bkmrk-namescientific-notat-1"><div id="bkmrk-namescientific-notat-2"><div><div class="container"><table class="__wikiTableVersion:Lion gridlines alternating" frame="box" rules="all" style="" width="1px"><tbody><tr><td class="cell" id="bkmrk-name"><div><div><div><div><div><span style="font-weight: bold;">Name</span>

</div></div></div></div></div></td><td class="cell" id="bkmrk-scientific-notation"><div><div><div><div><div><span style="font-weight: bold;">Scientific Notation</span>

</div></div></div></div></div></td><td class="cell" id="bkmrk-prefix-name"><div><div><div><div><div><span style="font-weight: bold;">Prefix Name</span>

</div></div></div></div></div></td><td class="cell" id="bkmrk-prefix-letter"><div><div><div><div><div><span style="font-weight: bold;">Prefix Letter</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-billion"><div><div><div><div><div>Billion

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%B9"><div><div><div><div><div>10⁹

</div></div></div></div></div></td><td class="cell" id="bkmrk-giga"><div><div><div><div><div>giga

</div></div></div></div></div></td><td class="cell" id="bkmrk-g"><div><div><div><div><div>G

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-million"><div><div><div><div><div>Million

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%B6"><div><div><div><div><div>10⁶

</div></div></div></div></div></td><td class="cell" id="bkmrk-mega"><div><div><div><div><div>mega

</div></div></div></div></div></td><td class="cell" id="bkmrk-m"><div><div><div><div><div>M

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-thousand"><div><div><div><div><div>Thousand

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%C2%B3"><div><div><div><div><div>10³

</div></div></div></div></div></td><td class="cell" id="bkmrk-kilo"><div><div><div><div><div>kilo

</div></div></div></div></div></td><td class="cell" id="bkmrk-k"><div><div><div><div><div>k

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-hundredth"><div><div><div><div><div>Hundredth

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%BB%C2%B2"><div><div><div><div><div>10⁻²

</div></div></div></div></div></td><td class="cell" id="bkmrk-centi"><div><div><div><div><div>centi

</div></div></div></div></div></td><td class="cell" id="bkmrk-c"><div><div><div><div><div>c

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-thousandth"><div><div><div><div><div>Thousandth

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%BB%C2%B3"><div><div><div><div><div>10⁻³

</div></div></div></div></div></td><td class="cell" id="bkmrk-milli"><div><div><div><div><div>milli

</div></div></div></div></div></td><td class="cell" id="bkmrk-m-1"><div><div><div><div><div>m

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-millionth"><div><div><div><div><div>Millionth

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%BB%E2%81%B6"><div><div><div><div><div>10⁻⁶

</div></div></div></div></div></td><td class="cell" id="bkmrk-micro"><div><div><div><div><div>micro

</div></div></div></div></div></td><td class="cell" id="bkmrk-%C2%B5"><div><div><div><div><div>µ

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-billionth"><div><div><div><div><div>Billionth

</div></div></div></div></div></td><td class="cell" id="bkmrk-10%E2%81%BB%E2%81%B9"><div><div><div><div><div>10⁻⁹

</div></div></div></div></div></td><td class="cell" id="bkmrk-nano"><div><div><div><div><div>nano

</div></div></div></div></div></td><td class="cell" id="bkmrk-n"><div><div><div><div><div>n

</div></div></div></div></div></td></tr></tbody></table>

</div></div></div></div></div>  
  
Example 1: 67MW = 0.067GW = 67,000kW = 67,000,000W

  

Example 2: 12cm = 0.12m = 120mm

### APES Chemical Formulas

Here are important chemical APES formulas to know:

<div class="table" id="bkmrk-common-namechemical-"><div id="bkmrk-common-namechemical--1"><div id="bkmrk-common-namechemical--2"><div><div class="container"><table class="__wikiTableVersion:Lion gridlines alternating" frame="box" rules="all" style="" width="1px"><tbody><tr><td class="cell" id="bkmrk-common-name"><div><div><div><div><div><span style="font-weight: bold;">Common Name</span>

</div></div></div></div></div></td><td class="cell" id="bkmrk-chemical-equation"><div><div><div><div><div><span style="font-weight: bold;">Chemical Equation</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-respiration"><div><div><div><div><div>Respiration

</div></div></div></div></div></td><td class="cell" id="bkmrk-c6h12o6%C2%A0%2B-6o2%C2%A0%E2%86%92-6co2"><div><div><div><div><div>C6H12O6 + 6O2 → 6CO2 + 6H2O

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-combustion"><div><div><div><div><div>Combustion

</div></div></div></div></div></td><td class="cell" id="bkmrk-hydrocarbons-%28cxhy%29-"><div><div><div><div><div>Hydrocarbons (CxHy) + O2 → CO2 + H2O

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-photosynthesis"><div><div><div><div><div>Photosynthesis

</div></div></div></div></div></td><td class="cell" id="bkmrk-6co2%C2%A0%2B-6h2o-%2B-sunlig"><div><div><div><div><div>6CO2 + 6H2O + sunlight → C6H12O6 + 6O2

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-ocean-acidification"><div><div><div><div><div>Ocean acidification

</div></div></div></div></div></td><td class="cell" id="bkmrk-co2%C2%A0%2B-h2o-%E2%86%94-h2co3%C2%A0%E2%86%94-"><div><div><div><div><div>CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3-

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-photochemical-smog-f"><div><div><div><div><div>Photochemical smog formation

</div></div></div></div></div></td><td class="cell" id="bkmrk-nox%C2%A0%2B-vocs-%2B-heat-%2B-"><div><div><div><div><div>NOx + VOCs + heat + sunlight → smog

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-stratospheric-ozone-"><div><div><div><div><div>Stratospheric ozone depletion

</div></div></div></div></div></td><td class="cell" id="bkmrk-o3%C2%A0%2B-cl-%E2%86%92-o2%C2%A0%2B-clo"><div><div><div><div><div>O3 + Cl → O2 + ClO

</div></div></div></div></div></td></tr></tbody></table>

</div></div></div></div></div>### List of Mathematical Routines

Here are the important mathematical routines:

<div class="table" id="bkmrk-common-namemathemati"><div id="bkmrk-common-namemathemati-1"><div id="bkmrk-common-namemathemati-2"><div><div class="container"><table class="__wikiTableVersion:Lion gridlines alternating" frame="box" rules="all" style="" width="1px"><tbody><tr><td class="cell" id="bkmrk-common-name-1"><div><div><div><div><div><span style="font-weight: bold;">Common Name</span>

</div></div></div></div></div></td><td class="cell" id="bkmrk-mathematical-formula"><div><div><div><div><div><span style="font-weight: bold;">Mathematical Formula</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-population-density"><div><div><div><div><div>Population density

</div></div></div></div></div></td><td class="cell" id="bkmrk-population%C2%A0area"><div><div><div><div><div><span style="font-style: italic;">Population</span> <span style="font-style: italic;">Area</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-rule-of-70"><div><div><div><div><div>Rule of 70

</div></div></div></div></div></td><td class="cell" id="bkmrk-70%C2%A0percent-growth-ra"><div><div><div><div><div>70 <span style="font-style: italic;">Percent growth rate</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-population-growth-ra"><div><div><div><div><div>Population growth rate as a percent

</div></div></div></div></div></td><td class="cell" id="bkmrk-births---deaths%C2%A0numb"><div><div><div><div><div><span style="font-style: italic;">Births - Deaths</span> <span style="font-style: italic;">Number of people</span> x 100

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-rate-of-change"><div><div><div><div><div>Rate of change

</div></div></div></div></div></td><td class="cell" id="bkmrk-final---initial%C2%A0fina"><div><div><div><div><div><span style="font-style: italic;">Final - Initial</span> <span style="font-style: italic;">Final time - Initial time</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-percent-change"><div><div><div><div><div>Percent change

</div></div></div></div></div></td><td class="cell" id="bkmrk-final--initial%C2%A0initi"><div><div><div><div><div><span style="font-style: italic;">Final -Initial</span> <span style="font-style: italic;">Initial</span> x 100

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-net-primary-producti"><div><div><div><div><div>Net Primary Productivity (NPP)

</div></div></div></div></div></td><td class="cell" id="bkmrk-gross-primary-produc"><div><div><div><div><div><span style="font-style: italic;">Gross primary productivity (GPP) - Respiration</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-gross-primary-produc-1"><div><div><div><div><div>Gross Primary Productivity (GPP)

</div></div></div></div></div></td><td class="cell" id="bkmrk-gpp-%3D-rate-of-photos"><div><div><div><div><div><span style="font-style: italic;">GPP = Rate of photosynthesis by plants</span>

  

<span style="font-style: italic;">GPP can also be expressed as:</span>

  

<span style="font-style: italic;">GPP = Total solar energy captured by plants − Energy lost due to respiration by plants</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-fuel-efficiency"><div><div><div><div><div>Fuel efficiency

</div></div></div></div></div></td><td class="cell" id="bkmrk-distance-traveled%C2%A0un"><div><div><div><div><div><span style="font-style: italic;">Distance traveled</span> <span style="font-style: italic;">Unit of fuel consumed</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-the-10%25-rule"><div><div><div><div><div>The 10% Rule

</div></div></div></div></div></td><td class="cell" id="bkmrk-the-10%25-rule-states-"><div><div><div><div><div><span style="font-style: italic;">The 10% rule states that roughly only 10% of energy transfers between trophic levels in a food chain, with the rest being lost as heat.</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-dimensional-analysis"><div><div><div><div><div>Dimensional Analysis

</div></div></div></div></div></td><td class="cell" id="bkmrk-quantity-1-x-convers"><div><div><div><div><div><span style="font-style: italic;">Quantity 1 x Conversion factor</span> <span style="font-style: italic;">Quantity 2</span> = <span style="font-style: italic;">Result</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-half-life"><div><div><div><div><div>Half-Life

</div></div></div></div></div></td><td class="cell" id="bkmrk-t%C2%BD%C2%A0%3D%C2%A0ln%C2%A0%282%29%C2%A0%CE%BB"><div><div><div><div><div><span style="font-style: italic;">t</span><span style="font-style: italic;">½ </span>= <span style="font-style: italic;">ln</span> (2) <span style="font-style: italic;">λ</span>

</div></div></div></div></div></td></tr><tr><td class="cell" id="bkmrk-ld50"><div><div><div><div><div>LD50

</div></div></div></div></div></td><td class="cell" id="bkmrk-ld50%C2%A0%3D-dose%C2%A0weight"><div><div><div><div><div>LD50 <span style="font-style: italic;">= Dose</span> <span style="font-style: italic;">Weight</span>

</div></div></div></div></div></td></tr></tbody></table>

</div></div></div></div></div><span id="bkmrk-common-namemathemati-3"><div>  
</div><div><span style="font-size: 11pt; font-family: Arial, sans-serif; font-weight: 700; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Common Name</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-weight: 700; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Mathematical Formula</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Population density</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Population </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">/ </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Area</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Rule of 70</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">70 / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Percent growth rate</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Population growth rate as a percent</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">( ( Births - Deaths</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> ) / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Number of people )</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> x 100</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Rate of change</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">( Final - Initial</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> ) / ( </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Final time - Initial time )</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Percent change</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">( Final - Initial )</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Initial )</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> x 100</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Net Primary Productivity (NPP)</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Gross primary productivity (GPP) - Respiration</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Gross Primary Productivity (GPP)</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">GPP = Rate of photosynthesis by plants</span>

  

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">GPP can also be expressed as:</span>

  

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">GPP = Total solar energy captured by plants − Energy lost due to respiration by plants</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Fuel efficiency</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Distance traveled</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Unit of fuel consumed</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">The 10% Rule</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">The 10% rule states that roughly only 10% of energy transfers between trophic levels in a food chain, with the rest being lost as heat.</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Dimensional Analysis</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Quantity 1 x ( Conversion factor</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Quantity 2 )</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">= </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Result</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Half-Life</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">t</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="font-size: 0.6em; vertical-align: sub;">½ </span></span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">= </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">ln</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> (2) / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">λ</span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">LD</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="font-size: 0.6em; vertical-align: sub;">50</span></span>

<span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">LD</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="font-size: 0.6em; vertical-align: sub;">50</span></span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">= Dose</span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"> / </span><span style="font-size: 11pt; font-family: Arial, sans-serif; font-style: italic; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;">Weight</span>

</div></span><span id="bkmrk--7"></span>  
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