<h2>Combinations of SI Base Units</h2>
To make working with units easier, some combinations of the base units are given special names, but it is always correct to reduce everything to the base units. The table below lists some examples of combinations of SI base units that are assigned special names. Do not be concerned if the formulae look unfamiliar at this stage - we will deal with each in detail in the chapters ahead (as well as many others)!
It is very important that you are able to recognise the units correctly. For example, the newton ($\text{N}$) is another name for the kilogram metre per second squared ($\text{kg·m·s$^{-2}$}$), while the kilogram metre squared per second squared ($\text{kg·m$^{2}$·s$^{-2}$}$) is called the joule ($\text{J}$).
<h3>Table: Some Examples of Combinations of SI Base Units Assigned Special Names</h3>
<div>
<table summary="">
<tbody>
<tr>
<td>
Quantity
</td>
<td>
Formula
</td>
<td>
Unit expressed in base units
</td>
<td>
Name of combination
</td>
</tr>
<tr>
<td>
Force
</td>
<td>
$ma$
</td>
<td>
$\text{kg·m·s$^{-2}$}$
</td>
<td>
$\text{N}$ (Newton)
</td>
</tr>
<tr>
<td>
Frequency
</td>
<td>
$\frac{1}{T}$
</td>
<td>
$\text{s$^{-1}$}$
</td>
<td>
$\text{Hz}$ (Hertz)
</td>
</tr>
<tr>
<td>
Work
</td>
<td>
$Fs$
</td>
<td>
$\text{kg·m$^{2}$·s$^{-2}$}$
</td>
<td>
$\text{J}$ (Joule)
</td>
</tr>
</tbody>
</table>
</div>
<h2>Prefixes of Base Units</h2>
Now that you know how to write numbers in scientific notation, another important aspect of units is the prefixes that are used with the units. In the case of units, the prefixes have a special use. The kilogram ($\text{kg}$) is a simple example. $\text{1}$ $\text{kg}$ is equal to $\text{1 000}$ $\text{g}$ or $\text{1} \times \text{10}^{\text{3}}$ $\text{g}$. Grouping the $\text{10}^{\text{3}}$ and the $\text{g}$ together we can replace the $\text{10}^{\text{3}}$ with the prefix k (kilo). Therefore the k takes the place of the $\text{10}^{\text{3}}$. The kilogram is unique in that it is the only SI base unit containing a prefix.
<div class="ns-school-defn2">
<h3>Tip:</h3>
When writing combinations of base SI units, place a dot (·) between the units to indicate that different base units are used. For example, the symbol for metres per second is correctly written as $\text{m·s$^{-1}$}$, and not as $\text{ms$^{-1}$}$ or $\text{m/s}$. Although the last two options is accepted in tests and exams, we will mostly use the first one.
</div>
In science, all the prefixes used with units are some power of $\text{10}$. The table below lists some of these prefixes. You will not use most of these prefixes, but those prefixes listed in bold should be learnt. The case of the prefix symbol is very important. Where a letter features twice in the table, it is written in uppercase for exponents bigger than one and in lowercase for exponents less than one. For example M means mega ($\text{10}^{\text{6}}$) and m means milli ($\text{10}^{-\text{3}}$).
<h3>Table: Unit prefixes</h3>
<div>
<table summary="">
<tbody>
<tr>
<td>
Prefix
</td>
<td>
Symbol
</td>
<td>
Exponent
</td>
<td>
Prefix
</td>
<td>
Symbol
</td>
<td>
Exponent
</td>
</tr>
<tr>
<td>
yotta
</td>
<td>
Y
</td>
<td>
$\text{10}^{\text{24}}$
</td>
<td>
yocto
</td>
<td>
y
</td>
<td>
$\text{10}^{-\text{24}}$
</td>
</tr>
<tr>
<td>
zetta
</td>
<td>
Z
</td>
<td>
$\text{10}^{\text{21}}$
</td>
<td>
zepto
</td>
<td>
z
</td>
<td>
$\text{10}^{-\text{21}}$
</td>
</tr>
<tr>
<td>
exa
</td>
<td>
E
</td>
<td>
$\text{10}^{\text{18}}$
</td>
<td>
atto
</td>
<td>
a
</td>
<td>
$\text{10}^{-\text{18}}$
</td>
</tr>
<tr>
<td>
peta
</td>
<td>
P
</td>
<td>
$\text{10}^{\text{15}}$
</td>
<td>
femto
</td>
<td>
f
</td>
<td>
$\text{10}^{-\text{15}}$
</td>
</tr>
<tr>
<td>
tera
</td>
<td>
T
</td>
<td>
$\text{10}^{\text{12}}$
</td>
<td>
pico
</td>
<td>
p
</td>
<td>
$\text{10}^{-\text{12}}$
</td>
</tr>
<tr>
<td>
giga
</td>
<td>
G
</td>
<td>
$\text{10}^{\text{9}}$
</td>
<td>
nano
</td>
<td>
n
</td>
<td>
$\text{10}^{-\text{9}}$
</td>
</tr>
<tr>
<td>
mega
</td>
<td>
M
</td>
<td>
$\text{10}^{\text{6}}$
</td>
<td>
micro
</td>
<td>
μ
</td>
<td>
$\text{10}^{-\text{6}}$
</td>
</tr>
<tr>
<td>
kilo
</td>
<td>
k
</td>
<td>
$\text{10}^{\text{3}}$
</td>
<td>
milli
</td>
<td>
m
</td>
<td>
$\text{10}^{-\text{3}}$
</td>
</tr>
<tr>
<td>
hecto
</td>
<td>
h
</td>
<td>
$\text{10}^{\text{2}}$
</td>
<td>
centi
</td>
<td>
c
</td>
<td>
$\text{10}^{-\text{2}}$
</td>
</tr>
<tr>
<td>
deca
</td>
<td>
da
</td>
<td>
$\text{10}^{\text{1}}$
</td>
<td>
deci
</td>
<td>
d
</td>
<td>
$\text{10}^{-\text{1}}$
</td>
</tr>
</tbody>
</table>
</div>
<div class="ns-school-defn2">
<h3>Tip:</h3>
There is no space and no dot between the prefix and the symbol for the unit.
</div>
Here are some examples of the use of prefixes:
<ul>
<li>$\text{40 000}$ $\text{m}$ can be written as $\text{40}$ $\text{km}$ (kilometre)</li>
<li>$\text{0.001}$ $\text{g}$ is the same as $\text{10}^{-\text{3}}$ $\text{g}$ and can be written as $\text{1}$ $\text{mg}$ (milligram)</li>
<li>$\text{2.5} \times \text{10}^{\text{6}}$ $\text{N}$ can be written as $\text{2.5}$ $\text{MN}$ (meganewton)</li>
<li>$\text{250 000}$ $\text{A}$ can be written as $\text{250}$ $\text{kA}$ (kiloampere) or $\text{0.250}$ $\text{MA}$ (megaampere)</li>
<li>$\text{0.000000075}$ $\text{s}$ can be written as $\text{75}$ $\text{ns}$ (nanoseconds)</li>
<li>$\text{3} \times \text{10}^{-\text{7}}$ $\text{mol}$ can be rewritten as $\text{0.3} \times \text{10}^{-\text{6}}$ $\text{mol}$, which is the same as $\text{0.3} \times \text{10}^{-\text{6}}$ $\text{μmol}$ (micromol)</li>
</ul>
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SI Base Units

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SI Base Units

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