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Unit Prefixes

Unit Prefixes

Many units are not convenient for using for all the uses we have for them. For example, the metre is not long enough to conveniently use for measuring long distances. The distance from Auckland to Tauranga is about 200,000 m. It is much more convenient to use a unit a thousand times as big as the metre - a kilometre - so that we can say Auckland to Tauranga is 200 km. Here "kilo" is a prefix to "metre" , and means a thousand.

Prefixes also allow us to easily do slightly weird things, like express the number of megaseconds in a year. (See the bottom of the page for the number.)

The capitalisation of prefixes is very important. More than a handful of mA (milliamps) is enough to kill you, but a MA (mega-amp) is enough to blow you apart, while a Ma (mega-annum) means something else again (millions of years).

With all prefixes the accent is on the first syllable. Hence kilometer, not kilometre.

The prefix always takes precedence over any exponentiation; thus "km2" means square kilometre and not kilo–square metre. For example, 3 km2 is equal to 3,000,000 m2 and not to 3,000 m2 (nor to 9,000,000 m2).

When using the symbol for a unit, an s is not added to the end to signify plural forms. In other words "10 m" is not written as "10 ms" because that then makes it "ten milliseconds". The problem is perhaps most common with the units km and cm, since some people think they are simply abbreviations, not symbols. Kilometre-seconds (kms) and centimetre-seconds (cms) are not very commonly used units.

The twenty SI (Système International) prefixes are shown in the chart below.

SI prefixes
1000m 10n Prefix Symbol Since[1] Short scale Long scale Decimal
10008 1024 yotta- Y 1991 Septillion Quadrillion 1,000,000,000,000,000,000,000,000
10007 1021 zetta- Z 1991 Sextillion Trilliard 1,000,000,000,000,000,000,000
10006 1018 exa- E 1975 Quintillion Trillion 1,000,000,000,000,000,000
10005 1015 peta- P 1975 Quadrillion Billiard 1,000,000,000,000,000
10004 1012 tera- T 1960 Trillion Billion 1,000,000,000,000
10003 109 giga- G 1960 Billion Milliard 1,000,000,000
10002 106 mega- M 1960 Million 1,000,000
10001 103 kilo- k 1795 Thousand 1,000
10002/3 102 hecto- h 1795 Hundred 100
10001/3 101 deca- da 1795 Ten 10
10000 100 (none) (none) NA One 1
1000-1/3 10-1 deci- d 1795 Tenth 0.1
1000-2/3 10-2 centi- c 1795 Hundredth 0.01
1000-1 10-3 milli- m 1795 Thousandth 0.001
1000-2 10-6 micro- 1960[2] Millionth 0.000 001
1000-3 10-9 nano- n 1960 Billionth Milliardth 0.000 000 001
1000-4 10-12 pico- p 1960 Trillionth Billionth 0.000 000 000 001
1000-5 10-15 femto- f 1964 Quadrillionth Billiardth 0.000 000 000 000 001
1000-6 10-18 atto- a 1964 Quintillionth Trillionth 0.000 000 000 000 000 001
1000-7 10-21 zepto- z 1991 Sextillionth Trilliardth 0.000 000 000 000 000 000 001
1000-8 10-24 yocto- y 1991 Septillionth Quadrillionth 0.000 000 000 000 000 000 000 001
  1. The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.
  2. The 1948 recognition of the micron by the CGPM was abrogated in 1967.

For more names of big numbers see names of large numbers.

Converting Units

As well as standard units, like metres and cubic meters, we have lots of other units that are sometimes used instead, like (the old unit of) feet and litres.

Converting from cubic metres to litres is easy, since the definition of the litre comes from the metre, but we can also work out a volume directly in litres by calculating the number of cubic decimeters in an object. Remember, a litre is 1 dm3 which is a cube 10 cm on a side.

For example, if we want to work out the volume in litres of a mattress which is 900 mm wide by 100 mm thick by 1800 mm long we could multiply these figures together (to make 162 million cubic millimetres) then divide by one million, or we could much more simply make the calculations using decimetres. Remember:

 1 m = 10 dm
1 dm = 10 cm 
 1 cm = 10 mm

9 dm x 1 dm x 18 dm = 162 dm3 = 162 L

To convert feet to metres - units which both describe length but do not simply relate to each other - we need to know the conversion factor. From the modern definition of an inch:

  1 inch = 25.4 mm
12 inches = 1 foot        

∴ 1 foot = 304.8 mm
∴ 1 m ≈ 39.37 inches or 3.28 feet

Calculating the number of seconds in a year is easier, as it's just a matter of multiplying the right numbers together. (Don't forget to add a quarter of a day for leap years.*) Using a prefix allows us to express it as the number of megaseconds in a year.

1 year           
= 365.25 days      
= 8766 hours        
= 525,960 minutes
= 31,557,600 s     
= 31,557.6 ks       
= 31.5576 Ms       

* Different calendars have different length years because of how they account for differences with the actual year length – leap days are a common method. The Julian Calendar used in astronomy is exactly 365.25 days long, but in the Gregorian Calendar (the most commonly used calendar for keeping track of dates) centuries which are not divisible by 400 are not leap years. For example, 1900 and 2100 are not leap years, but 2000 is. That means taking off another 3 days every 400 years, making 365.2425 days per year. That's very close to the length of the March equinox year of 365.242374 days it was designed to fit (although the mean tropical year is slightly shorter at 365.24217 mean solar days).