## Principles of the Metric System

Everything in metric is based on sensible and easy to understand principles, i.e. that prefixes for units are based on 10, 100, 1000, 1 million, 1 billion, or fractions of one tenth, one hundredth, one thousandth, one millionth, and so on.

There are base units, and other units used in metric are based on these, and a lot of units are inter-related.

This image shows a ruler of length 1 metre, with 10 decimetre subdivisions, shown against a public drinking tap. This should give you some idea of how long 1 metre is.

Each decimetre is equal to 10 centimetres, and this is the same as 100 millimetres, and it is one tenth of 1 metre.

Volume is cubic, i.e. length multiplied by height multiplied by width, so we get a volume measured in cubic centimetres, which is written as cm^{3}.

Then, using cubic centimetres to measure volume, if you have a cube that measures 1 cm by 1 cm by 1 cm, this would be 1 cm^{3} in volume.

Take 1000 of these together, and then call this 1 litre, giving a unit for volume. Also if we take a cube which has sides of 10 cm each, it has a volume of 10 × 10 × 10 = 1000 cm^{3} = 1000 millilitres = 1 litre.

### 1 litre of water weighs 1 kilogram

Then we take this new measurement and take some pure water at a temperature of 3 °C, measure out 1 litre of it, and then measure its mass, and we define that as 1 kilogram. So we see how length volume and mass (weight) are all related so easily. In practice we can remember that 1 litre of water weighs 1 kg, so that if you go to the supermarket and buy a bottle of water, and the label has “2 litres” written on the side, then it will weigh 2 kilograms. Useful to know if you are going to be carrying it home by hand!

1 litre of water weighs 1 kg at room temperature. The image above shows this, although we have not taken into account the weight of the bottle, which would be a few grams.

### Prefixes

All prefixes in metric are standard and follow a logical pattern. 1000 of a unit will have the prefix kilo, 1 000 000 will have the prefix mega.

## k = kilo = 1 000

## M = mega = 1 000 000

We have put them all in a table below: Note that the 10 with a small number after it represents mathematical notation, and it is easy to figure out.

A positive number after the 10 represents how many noughts the prefix replaces, e.g. 10^{6} means that the prefix mega can be used for any unit which has values in millions, i.e. 1 000 000 watts = 1 megawatt, i.e. we have knocked off the last 6 numbers and changed the unit by adding mega. We could also do it to numbers without noughts, e.g. 2 345 543 watts = 2.345 543 megawatts — note the position of the decimal point here.

*In the table we have listed all prefixes as agreed at the 19th General Conference on Weights and Measures in 1991, and some of these you will not use in normal everyday life. The most common ones are highlighted in yellow.*

## Prefix |
## Symbol |
## Value |
## Value name |

yotta | Y | 10^{24} |
1 septillion |

zetta | Z | 10^{21} |
1 sextillion |

exa | E | 10^{18} |
1 quintillion |

peta | P | 10^{15} |
1 quadrillion |

tera | T | 10^{12} |
1 trillion |

giga | G | 10^{9} |
1 billion |

mega | M | 10^{6} |
1 million |

kilo | k | 10^{3} |
1 thousand |

hecto | h | 10^{2} |
1 hundred |

deca | da | 10^{1} |
ten |

deci | d | 10^{-1} |
1 tenth |

centi | c | 10^{-2} |
1 hundredth |

milli | m | 10^{-3} |
1 thousandth |

micro | µ | 10^{-6} |
1 millionth |

nano | n | 10^{-9} |
1 billionth |

pico | p | 10^{-12} |
1 trillionth |

femto | f | 10^{-15} |
1 quadrillionth |

atto | a | 10^{-18} |
1 quintillionth |

zepto | z | 10^{-21} |
1 sextillionth |

yocto | y | 10^{-24} |
1 septillionth |

More information on metric prefixes can be found at

https://www.bipm.org/en/measurement-units/si-prefixes

Note as well that some of the prefixes are UPPER CASE and some are lower case, this is very important in writing prefixes, as the prefix for yotta (Y) is not the same as that for yocto (y), the difference is quite huge, the same applies to mega (M) and milli (m) where the use of a lower case m in place of M would cause confusion. This sometimes happens with computing terms, which uses metric units and prefixes, such as in the abbreviation for megabytes, which is correctly written as MB and not as mB or mb. Mb means megabits. mB would mean millibytes and mb would mean millibits, although such units do not actually exist.