For example, 75 kilometres = 75km∗1 000mkm{\displaystyle 75km*1\ 000{\frac {m}{km}}} = 75 000 metres. To make sure you’ve set up the conversion correctly, try reading it in plain English: 1000mkm{\displaystyle 1000{\frac {m}{km}}} means “1 000 metres per kilometre”.
75 kilograms (kg) = 75kg∗1 000gkg{\displaystyle 75kg1\ 000{\frac {g}{kg}}} = 75 000 grams (g). [3] X Research source 14 kilowatts (kW) = 14kW∗1 000WkW{\displaystyle 14kW1\ 000{\frac {W}{kW}}} = 14 000 watts (W). [4] X Research source
A 3 megawatt (MW) factory produces 3MW∗1 000 000WMW{\displaystyle 3MW1\ 000\ 000{\frac {W}{MW}}} = 3 000 000 watts (W) of power. A 2 gigajoule (GJ) explosion releases 2GJ∗1 000 000 000JGJ{\displaystyle 2GJ1\ 000\ 000\ 000{\frac {J}{GJ}}} = 2 000 000 000 joules (J) of energy.
65 300 metres is equal to 65 300m∗1 km1 000m{\displaystyle 65\ 300m*{\frac {1\ km}{1\ 000m}}} = 65. 3 kilometres.
centi- (c) means “one hundredth” (0. 01). 1 centimetre = 0. 01 metres. milli- (m) means “one thousandth” (0. 001). 1 millimetre = 0. 001 metres. micro- (µ) means “one millionth” (0. 000 001). 1 micrometre = 0. 000 001 metres. nano- (n) means “one billionth” (0. 000 000 001). 1 nanometre = 0. 000 000 001 metres.
Centimetres to metres: 33 centimetres = 33cm∗0. 01mcm{\displaystyle 33cm0. 01{\frac {m}{cm}}} = 0. 33 metres. Metres to millimetres: 2. 15 metres = 2. 15m∗1mm0. 001m{\displaystyle 2. 15m{\frac {1mm}{0. 001m}}} = 2150 millimetres.
Check the units in your equation. If you set it up correctly, the original units should cancel out. For example 75km∗1000mkm{\displaystyle 75km1000{\frac {m}{km}}} gives you an answer in terms of km∗mkm{\displaystyle {\frac {kmm}{km}}}. The km units are on top and bottom, so they cancel out and leave you with m (metres). Compare the units logically. The smaller unit should always have the larger number next to it. Metres are smaller than kilometres, so it takes more of them to fill the same length. For example, a result of 75 000 metres = 75 kilometres makes sense, since a larger number of metres equals a smaller number of kilometres.
giga- = 1 000 000 000 = 109 mega- = 1 000 000 = 106 kilo- = 1 000 = 103 centi- = 0. 01 = 10-2 milli- = 0. 001 = 10-3 micro- = 0. 000 001 = 10-6 nano- = 0. 000 000 001 = 10-9 You can also write a negative exponent as a fraction with a positive exponent in the denominator: 10−2=1102{\displaystyle 10^{-2}={\frac {1}{10^{2}}}}
Example: How many centimetres are in 13. 78 kilometres?The answer isn’t obvious, but you do know that the kilometre is equal to 103 metres. Therefore, 13. 78 km = 13. 78 * 103 metres. You’ll use this in the next step.
To continue the example, you know want to convert 13. 78 * 103 metres into centimetres. The prefix centi- means 10-2, so there is 1cm10−2m{\displaystyle {\frac {1cm}{10^{-2}m}}}
13. 78∗103m∗1cm10−2m=13. 78∗10310−2 {\displaystyle 13. 7810^{3}m{\frac {1cm}{10^{-2}m}}={\frac {13. 78*10^{3}}{10^{-2}}}\ } cm
13. 78∗10310−2{\displaystyle {\frac {13. 7810^{3}}{10^{-2}}}} cm = 13. 78∗103−(−2)=13. 78∗105{\displaystyle 13. 7810^{3-(-2)}=13. 7810^{5}} centimeters. It’s usually helpful to write your answer in scientific notation (standard form): 1. 378∗106{\displaystyle 1. 37810^{6}} centimeters.
Write the initial prefix and the final prefix as powers of 10. For base units without prefixes, use 100{\displaystyle 10^{0}}. Divide the initial power of 10 by the final power of 10. (To do this, subtract the final exponent from the initial exponent. ) Multiply your initial value by this answer. Example: How many centilitres (cL) are in 85 500 millilitres (mL)?The initial prefix is “milli-” = 10−3{\displaystyle 10^{-3}} and the final prefix is “centi-” = 10−2{\displaystyle 10^{-2}}. 10−310−2=10(−3)−(−2)=10−1{\displaystyle {\frac {10^{-3}}{10^{-2}}}=10^{(-3)-(-2)}=10^{-1}}85 500 millilitres = 85 500∗10−1{\displaystyle 85\ 50010^{-1}} centilitres. Optionally, write this in scientific notation: 8. 55∗103{\displaystyle 8. 5510^{3}} centilitres.
