Do you square the units when calculating numerically?

[ehrenfest]

[SOLVED] squaring units

Homework Statement

When you calculate numerically something like q^2/4*Pi*Epsilon_0, do you square the units of q i.e. is it (q 1.602 176 487 × 10-19 C)^2 or q^2 1.602 176 487 × 10-19 C ?

Homework Equations

The Attempt at a Solution

 

[malawi_glenn]

if q = 1.602*10^-19C, then q^2 = {(1.602*10^-19)^2}C^2

 

[Mute]

A good way to see that you have to square units (or raise them to any power) is to consider the following "paradox".

Suppose you have $1. One dollar is just 100 cents:

$1 = ¢100

If we take the square root of both sides but neglect to take the square root of the units (dollars and cents), we get

$1 = ¢10!

So, you have to take the square root of the units too, otherwise all of your dollars are only worth dimes, and all of your dimes are worth a dollar! (As attractive as that might sound, what do you want to bet that the banks would only treat your dollars as being dimes and not vice versa?)