Mastering SI-Prefix Conversions for Easy Homework Help

[bluepilotpen]

Homework Statement

My question doesn't really fit into the template here, but I'll give it a shot, anyway.

How do you go about converting SI-prefixes? I understand you're supposed to convert the prefixes into associated power of ten's, but then I'm stuck. How do you continue? Sometimes I get it right, sometimes wrong.

Any help would be much appreciated. Thanks! Oh, and sorry if I posted this in the wrong section. I blame it on a bad night's sleep.

Homework Equations

The problem could look like this:

Convert 4 uL (microlitres) to mL (millilitres).

The Attempt at a Solution

 

[Slats18]

Try it this way:

Convert 8L (litres) into ml (millilitres).

8L * (1000ml/1L) = 8000ml

See what happened? You've got a unit, L, for your 8 litres, and you want to change that into ml, so you multiply it by ml/L, as you know that there are 1000ml in a litre. You're essentially multiplying by 1, which doesn't change anything =)

 

[QuarkCharmer]

Your example:
Convert 4 uL (microlitres) to mL (millilitres)

The easiest way to go about this is to apply a unit factor/conversion. When I was in the military they taught me a good little (albeit non p/c) mnemonic.

Texas Girls Must Know Base Marines Use No Protection

T G M k base m u n p

Just remember that each one of those (working out from the base) is 3 more to the exponent.
So T is 10^12, and m is 10^3 etc..

Aside from that, you have to remember deci and centi between the base and m.

For your example, take the given value and apply a unit factor:

$$4uL\frac{1L}{10^6 uL}$$

This gives you the "base", and you must them convert it to mL by multiplying in another unit factor.

$$4uL\frac{1L}{10^6 uL}\frac{10^3 mL}{1L} = .004 mL$$
Pay close attention to the unit, and treat it like a variable. When you want to convert from one to the other, apply the unit factor in such a way where the original unit cancels out.

 

[I like Serena]

Both SI prefixes and units are items that you multiply with.

In your example you have:

4 uL
= 4 x micro x L
= 4 x 10^-6 x L
= 4 x 10^-3 x 10^-3 x L
= 4 x 10^-3 x milli x L
= 4 x 10^-3 mL