# Prefixes

concept
When dealing with the values in electrical circuits we often have to use numbers from 0.0000001 to 1000000. Sometimes we use numbers of both extremes in the same circuit for different things. This becomes tedious and difficult to use. It's also error prone since so many zeros makes leaving one off or adding one on easy to do and can wreak havok on your answers. To fix this we use simple prefixes before the units of a number to indicate how big or small it is without having to write out all the zeros. You're almost certainly used to using some of these prefixes already. The kilo, mega and giga are (almost) the same as the ones you use when talking about data usage on the internet. Working with prefixes is awkward and a real pain at first but it makes everything much, much simpler as you get into more advanced work, don't worry too much about memorising the different letters and their values, just keep a table written next to you as you do your work and you'll automatically pick it up eventually.
fact
Each prefix is a single letter and represents $$\times 10^x$$ where $$x$$ is a number determined by the letter of the prefix.
fact
The following table lists the most common prefixes and what they represent as well as their full names.
Symbol Multiplier Full Name
n $$\times 10^{-9}$$ nano
u (or $$\mu$$) $$\times 10^{-6}$$ micro
m $$\times 10^{-3}$$ milli
k $$\times 10^{3}$$ kilo
M $$\times 10^{6}$$ mega
G $$\times 10^{9}$$ giga
fact
Prefixes always come at the end of a number but before the unit. They're called prefixes because they prefix the unit, not the number.
example

Expand 10k

We just replace the 'k' with $$\times 10^3$$ to get $$10\times10^3 = 10000$$
example

Expand 1u

Looking up 'u' in the table we see that our number becomes $$1\times 10^{-6} = 0.000001$$
example

Expand 1.23M

'M' is $$\times 10^6$$ so 1.23M $$= 1.23\times 10^6 = 1230000$$
example

Simplify 1000

When we simplify numbers using prefixes we want to pick the prefix that makes the number out front between 1 and 1000. In this case the prefix 'k' is exactly the number we need so we can say $$1000 = 1k$$
example

Simplify 1300

Now to find the right number and prefix we divide our 1300 by various prefixes until we get a number between 1 and 1000. As you can probably see if we again choose 'k' we get $$\frac{1300}{k} = 1.3 \implies 1300 = 1.3k$$
practice problems