# Chapter 5: Scientific notation and SI units

A criticism of the International System of Units (SI units) is they frequently involve numbers too big or too small to use conveniently. This is commonly seen in biology where the size of biological components and their concentrations can be very small and the difference in the magnitude of different components can be huge (see **Chapter 4****:**** Biological ****s****cale**). If a number needs to be expressed with a very long chain of zeros, it will take longer to record or write down, and there is a larger chance of a mistake.

One way to get around this is to use scientific notation, in which very large or small numbers are written as two numbers multiplied together (usually exponents of base 10). For example, 3,000,000 m could be written as 3 × 10^{6} m and 0.000000005 mol could be rewritten as 5 × 10^{–}^{9} mol.

Another common way to express larger or smaller numbers is to make the unit larger or smaller using prefixes. You will be familiar with some of these, such as kilo (k, 10^{3}), milli (m, 10^{–}^{3}) and centi (c, 10^{–}^{2}).

Most of the prefixes adjust the unit by increments of three decimal places. That is, they involve 1,000-fold increases or decreases in scale.

**B****ecome familiar with the prefixes in the table below. Learn their names**** and ****symbols ****so that you can**** easily convert between them.**

Symbol |
Name |
Notation |
Factor |

T | tera | 10^{12} |
1,000,000,000,000 |

G | giga | 10^{9} |
1,000,000,000 |

M | mega | 10^{6} |
1,000,000 |

k | kilo | 10^{3} |
1,000 |

d | deci | 10^{–}^{1} |
0.1 |

c | centi | 10^{–}^{2} |
0.01 |

µ | micro | 10^{–}^{6} |
0.000001 |

n | nano | 10^{–}^{9} |
0.000000001 |

p | pico | 10^{–}^{12} |
0.000000000001 |

f | femto | 10^{–}^{15} |
0.000000000000001 |

a | atto | 10^{–}^{18} |
0.000000000000000001 |

### What are SI units?

SI stands for Système International d’Unités. This system, initially known as the metric system, was developed in France after the French Revolution and has now been adopted internationally. At first it consisted of three units – the metre, the kilogram and the second – but eventually expanded to include seven principle (basic) units. There are many more SI recognised units, but they are all derived from these basic seven units (e.g. the SI unit for force is the newton, N, which is derived from kg.m.s^{–2})

Quantity |
Unit |
Symbol |
---|---|---|

Length | metre | m |

Mass | kilogram | kg |

Time | second | s |

Electric current | ampere | A |

Temperature | kelvin | K |

Quantity of substance | mole | mol |

Luminosity | candle | cd |

##### Note

The litre is a non-SI unit which has been accepted as a measure for volume. Its symbol is either l or L. We’ve used L in this book as it can be easier to read, although it’s conventional for prefixed units to use lowercase (e.g. ml or dl).