dealing with really big and really small numbers

You have already met prefixes in your 109 maths workshop 1. These are going to be coming up lots more, so I thought I'd say a few words on the subject....

Prefixes help us deal with really big numbers and really small numbers, like:

198000 g 
or
0.0000000456 g

There are two ways you can write numbers like these more neatly. One way is to use powers of 10, i.e.

1980000000 g could be written as 1.98 x 10⁹ g
or

 0.0000000456 g could be written as 4.56 x 10^-8 g

The other way is to use prefixes. A prefix is simply a symbol you combine with the unit to represent multiples or fractions of that unit. Let me show you what I mean with a simple example:

1 kg

The 'k' or 'kilo' bit here is the prefix.

'k' represents a multiple of a thousand

So 1 kg is the same as saying 1 x 1000 g

i.e. 1 kg = 1000 g

Lets have another example:

1 mg

The 'm' or 'milli' bit here is the prefix.

'm' represents a division of a thousand

So, 1 mg is the same as saying 1/1000 g

i.e.  1 mg = 0.001 g

There are a number of prefixes that we tend to use quite a lot in Biology, these are:

M or mega - represents a multiple of 1000000 
(i.e. 1Mg = 1000000g)

k or kilo  - represents a multiple of 1000 
(i.e. 1kg = 1000g)

your unit without a prefix (i.e. g)

m or milli  - represents a division of 1000 
(i.e. 1mg = 0.001g)

μ or micro  - represents a division of 1000000 
(i.e. 1μg = 0.000001g)

n or nano  - represents a division of 1000000000 
(i.e. 1ng = 0.000000001g)

So if we had 5 g, we could write this as:

0.000005 Mg

0.005 kg

5 g

5000 mg

5000000 μg

5000000000 ng

So, if you have 2 ng, and you want write that in grams, you could do 2 / 1000000000 = 0.000000002 g. I actually don't like to work like this, I prefer to jump between adjacent prefixes like this:

2 ng / 1000 = 0.002μg

then

0.002 μg / 1000 = 0.000002 mg

then

0.000002 mg / 1000 = 0.000000002 g

But, what if you know you have 0.000000002g and you want to write this as ng? Then you could do 0.000000002g x 1000000000 = 2ng. Again, to work this out I prefer to jump between adjacent prefixes like this:

0.000000002 g x 1000 = 0.000002 mg

then

0.000002 mg x 1000 = 0.002 μg

then

0.002 μg x 1000 = 2 ng

Don't be scared of prefixes. Just remember what they mean, and remember what order they come in: M, k, m, μ, n. They can be put at the front of any unit, like μL or km.

This is a long post for something that is actually really simple! Hope it helps...