Chapter 3: Measurement

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 (kilometer) is one thousand meters. The following table gives the common metric prefixes that we will be using in this book:

kilo-k1 000
milli-m1/1 000
micro-μ1/1 000 000
Table of the metric prefixes commonly used in this book.

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.

MeasurementBase unitAbbreviationExample
Lengthmeterm65 m ≈ width of a soccer field
Masskilogramkg65 kg ≈ mass of an adult human
Timeseconds60 s = 1 minute
Summary of the base units of the SI system

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 103.” So 42 km is 42×103 m, or 42 000 m. The table below gives the powers of ten associated with commonly-used metric prefixes.

PrefixPower of ten
Powers of ten for common metric prefixes