Propagation of error if one of the values is 0

[nietzsche]

I'm doing a lab write-up and I've run into a snag. I'm trying to do propagation of error in a product, but one of my quantities that I'm multiplying is 0. The propagation of error formula for z = xy is

$$\left ( \frac{\Delta z}{z} \right )^2 = \left( \frac{\Delta x}{x} \right )^2 + \left (\frac{\Delta y}{y} \right )^2$$

But if either x or y = 0, what happens?

 

[RoyalCat]

Is it 0 by definition or is that just a measurement with low accuracy?

 

[nietzsche]

it's the velocity of a cart that was measured by a motion sensor, so it's a measurement. the value is 0.00 +/- 0.005.

 

[Delphi51]

If you look into the partial derivative definition used to find that error propagation formula, you will see that x = 0 makes the infinite term disappear. See
http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html#muldiv

 

[nietzsche]

thank you. i haven't learned partial derivatives yet, so i'll have to take your word for it.