# Homework Help: Percent weight and particle size

1. Dec 9, 2011

### zmike

Is there a difference between percent weight and percent number? I am working with particle size and I am really confused because I would expect that they would be the same?

eg.
WEIGHT----Number of particles
5---3
2---1
8---1

% weight of 3 would be 3*5/(5*3+2*1+8*1) = 60%?
% number of 3 would be 3/5 = 60%

Is this right? Are they always suppose to be the same? If there's the same then why do we need 2 different measurements??

THANKS!!
thanks

2. Dec 10, 2011

### cepheid

Staff Emeritus
Yes there is a difference. What you're calling "percent weight" is the percentage of the total weight contributed by particles of a given type. "Percent number" is the percentage of the total number of particles contributed by particles of a given type. They are measuring two totally different things. In general, they will be different, unless if all types of particles present have the same weight.

Why do you expect that they would be the same?

Even in this example you give, particles of the type in the second row (The type that has a particle weight of "2") make up 1/5 = 20% of the total number of particles. But they make up 2/(15 + 2 + 8) = 2/(25) = 8% of the total weight.

The third type of particle makes up 1/5 = 20% of the total number of particles. But they make up 8/25 = 32% of the total weight.

So, as you can see, in general, percentage by number and percentage by weight are NOT the same, and it was only coincidence that they happened to be the same for the first type of particle in this example.