How to find the number of excess electrons?

[pebbles]

Homework Statement

How many excess electrons are on a ball with a charge of -4.00*10^-17 C?

Homework Equations

I know that the charge per electron is 1.60 *10^-19C.

The Attempt at a Solution

My textbook does not explain how to do this, but I thought I would divide-->4.00*10^-17 C * 1 electron/-1.60*10^-19. I got -2.5*10^-36. The answer from the book is 2.5*10^2 electrons.
I did some messing around and did this-->4.00*10^-17C*1 e/1.60*10^19C=2.5*10^2 electrons.
What's the correct way to do this problem?
Thanks in advance.

 

[dynamicsolo]

Your set-up is right and the units will check. But how do you divide

4.0 x 10^-17 / 1.6 x 10^-19 ?

What is 1 / 1.6 x 10^-19 ?

(In fact, your check is also incorrect. You may want to review how division works with powers of ten and what negative exponents mean. 10^-17 / 10^-19 = 100 ; 10^-17 / 10^19 = 10^-36 .)

 

[pebbles]

uhh, I'm confused....?

 

[dynamicsolo]

You're dividing by 1.6 x .0000000000000000001 . So 4 / 1.6 is 2.5 , but what is

10^-17 / 10^-19 =

0.00000000000000001 / 0.0000000000000000001 ?

 

[pebbles]

oh i see!
10^-17/10^-19=100
so therefore 2.5*10^2.
thanks so much! :D

 

[Feldoh]

Charge is quantized so the excess charge has to be a multiple of e (elementary charge)

q=ne, where n is the number of electrons.

That's why it works I believe since your textbook didn't explain it.