Please help - converting units ?

[claire kt]

Please can someone explain to me how you convert:
10 micrograms per decilitre
into
miiligrams per litre

I think I had some notes on it somewhere but they have gone awol !

[Inspector Gadget]

Easiest way for multiple units (something per something) is using "fenceposts", as some teachers call them, which basically look like this...

\frac{10 micrograms}{1 deciliter} \times \frac{10 deciliters}{1 liter} \times \frac{1000 milligrams}{1000000 micrograms}

NOTE: I don't remember exactly what micrograms are...it's either 1 g x 10^6 or 1g x 10^9...I think it's 6, 9 is nano.

But basically what you have there is one giant fraction. The first fraction in the multiplication is your original given information, and all the other fractions within are equal to 1.

So, that fraction simplifies to \frac {1 milligram}{10 liters}

So, 10 micrograms per decilitre = 1/10 milligrams per liter.

Someone may wanna just double check on what exactly a microgram is in relationship to a gram...it's been so long since I've had to do that, I can't remember for sure. If I am wrong, that "fencepost" concept should be a pretty easy one to understand and remember for future use.

[NSX]

Please can someone explain to me how you convert:
10 micrograms per decilitre
into
miiligrams per litre

I think I had some notes on it somewhere but they have gone awol !

Use the Factor Label Method.

What is awol?

[claire kt]

Thanks Inspector Gadget.
You are right micro is -3 and nano -9.

NSX AWOL = absent with out leave. Half my notes have just completely vanished !

[HallsofIvy]

"micro" is 10-6 (one millionth)

[Muzza]

Yes, and 10^-3 is milli...