I'm completely confused. I know all the stuff about converting, say meters and kilometers, centimeters, etc. But what do I do about problems like "56.78 nm = ______ micrometers" ?

And I have all the SI factors, like how nano things factor to be 10^-9 or how kilo things are 10^3 and all that.

But I'm so lost, like kL to GL, Tg to g, and a million more units. Help?

## Answers (2)

First you must have on your mind the descending step - chain- line of SI factors and inverse.

Second how many times bigger or smaller is a factor from next or previous. So from bigger to smaller you multiply as many times shows the factor or inverse divide. General rule :

1) From base to smaller factors the 3-first there is a 10 times relation to each-one and then 1000 = 10^3 times bigger.

2)From base to Larger factors the 3-first are 10 times each-one and then 1000 = 10^3 times smaller.

The scale from base unit to smaller is:

1m -> 1dm -> 1cm -> 1mm -> 1um -> 1nm -> 1pm-> ......

1m = 10dm =100cm = 1000mm= 1,000,000um= 1,000,000,000nm=....

Now look at the position of nm and μm=micrometers in the upper scale. Which of them is bigger and how many times ? What is the wanted convertion from bigger to smaller or inverse?

Ans.: 1μm is bigger 1000 times from nm that is 1μm=1000nm =10^3nm or inverting

1nm is smaller 1000 times from μm that is 1nm=1/1000um =10^-3μm

So the wanted conversion is 56.78nm = 56.78/1000μm =0.05678μm

or 56.78*10^-3μm =5.678*10^-3μm

By the same way working the scale from larger factors to base unit is:

....->1GL ---> 1ML -----> 1kL -----> 1heL ----> 1daL ----> 1L

x1000 x1000 x10 x10 x10

In example kL->GL bigger is GL from kL 1000x1000=1,000,000 times or 10^6

so 1kL is 1000x1000=1,000,0000 smaller from GL That is 1kL=1/1,000,000GL or 1*10^-6GL

I would suggest going through the base unit. i.e. nm ==> m ==> um

Example: 56.78 nm = _____ um

56.78 nm x (1 m / 10^9 nm) x (10^6 um / 1 m) = 0.05678 um