## 3.3 The SI system

The metric system is used by every country in the world except for Liberia, Myanmar, and the United States of America. In the metric system, you have a *base* unit that tells you what kind of quantity is being measured and a **prefix** that tells you the scale. For example, a *meter* is a measurement of distance, and the prefix **kilo** means thousand; so a kilometer (**kilo***meter*) is one thousand meters. The following table gives the common metric prefixes that we will be using in this book:

Prefix | Abbreviation | Meaning |
---|---|---|

kilo- | k | 1 000 |

centi- | c | 1/100 |

milli- | m | 1/1 000 |

micro- | μ | 1/1 000 000 |

The scientific community uses a particular variety of the metric system called the *Système International d’Unités*, or SI. The difference between SI and other varieties of the metric system lies in how the base units are defined. The base units in the SI system are the meter for length, the kilogram for mass, and the second for time (it is sometimes called the *mks* system). This is summarized, with examples, in the following table. This is a very elegant system: whenever we see a prefix in front of a base unit, we automatically know the scale we’re dealing with, and the physical quantity being measured. By convention, the prefix **centi** is generally only used in length measurements with SI units.

Measurement | Base unit | Abbreviation | Example |
---|---|---|---|

Length | meter | m | 65 m ≈ width of a soccer field |

Mass | kilogram | kg | 65 kg ≈ mass of an adult human |

Time | second | s | 60 s = 1 minute |

### 3.3.1 Powers of ten

The defining characteristic of any variety of the metric system is that units scale in multiples of ten. This makes calculations and conversions very straightforward, and lends itself to a system of notation called *scientific notation*, which provides a convenient method of writing down very large and very small numbers.

A quantity is written in scientific notation by expressing it as a product of a number between 1 and 10, and a multiple of ten. For example,

\[ 42\thinspace000 = 4.2 \times 10^4 \]

For decimals, we use negative exponents:

\[ 0.000\thinspace42 = 4.2 \times 10^{-4} \]

Now we can write our metric prefixes as powers of ten, and each metric prefix means “multiply by 10 to some power.” For example, *kilo-* means “multiply by 10^{3}.” So 42 km is 42×10^{3} m, or 42 000 m. The table below gives the powers of ten associated with commonly-used metric prefixes.

Prefix | Power of ten |
---|---|

kilo- | 10^{3} |

centi- | 10^{-2} |

milli- | 10^{-3} |

micro- | 10^{-6} |