Formula to calculate the uncertainty in the density

[GlobalDuty]

Homework Statement

A radius of a sphere is measured to be (6.45 ± 0.27) cm, and the mass is measured to be (1.78 ± 0.09) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

Homework Equations

Use the following formula to calculate the uncertainty in the density:
Δρ/ρ = Δm/m + 3Δr/r.)

The Attempt at a Solution

I already found the density: 1583.62 kg/m3
I just want to know how to get the uncertainty. I don't know how to use the formula given. i always get a really low number with it.

 

[cepheid]

Welcome to PF!

The uncertainties are the ranges by which the measured quantities can vary, and these ranges are indicated using the symbol 'Delta.' Hence:

Δr = 0.27 cm

Δm = 0.09 kg

and of course, the measured values are:

r = 6.45 cm

m = 1.78 kg

 

[GlobalDuty]

This is what i did after converting to meters:
(0.09/1.78)+(3*.0027/.0645)

 

[Stonebridge]

0.17614 = Δρ/ρ so you don't need to divide by anything.
To find the actual uncertainty in p you multiply 0.17614 by the density you have calculated.
.

 

[GlobalDuty]

ok, thank you.