# Error calculation

## Homework Statement

a = 0.00083 ± 0.00002m

what is 1/a with error

## Homework Equations

rules for combining errors

z = xy or z=x/y σ(z) = [σ(x)]2[σ(y)]2

## The Attempt at a Solution

I tried doing 1/a ± 1/error

but the error gets too big... is there a rule for this kind of situation?

gneill
Mentor

## Homework Statement

a = 0.00083 ± 0.00002m

what is 1/a with error

## Homework Equations

rules for combining errors

z = xy or z=x/y σ(z) = [σ(x)]2[σ(y)]2

## The Attempt at a Solution

I tried doing 1/a ± 1/error

but the error gets too big... is there a rule for this kind of situation?

The rule for Z = X*Y or Z = X/Y is
$$\Delta Z = Z\sqrt{\left(\frac{\Delta X}{X}\right)^2 + \left(\frac{\Delta Y}{Y}\right)^2}$$
A rule for powers of a value:

If ##Z = X^n## then
$$\Delta Z = n x^{(n - 1)} \Delta X$$
In your case n = -1.

Can you present your calculations showing that your error result is too large? (and too large as compared to what?)