Volume/cm3 = (3.1 ± 0.1)cm3 x (3.1 ± 0.1)cm3 x (3.1 ± 0.1)cm3
Relative uncertainty = = = 0.032258064
As we are finding the volume, we need to add the uncertainties of all the measurements, i.e. length, width and height. In this case the material was a cube, where the measurements were the same and even the uncertainties, thus we can multiplied the uncertainty by 3, i.e.
0.032258064 x 3 = 0.0967741935
When converted in percentage we get: 9.677% ≈ 10%
Volume = 3.1cm x 3.1cm x 3.1cm = 29.791 cm3
Converting it to two significant figures, we obtain,
3.0 x 101 cm3 ± ≈10% = 3.0 x 101 cm3 ± 0.1
Therefore,
Density = =
Now add the uncertainties, i.e. 0.0004 + 0.1, which gives 0.1004, which if rounded off to one significant figure is 0.1. Dividing 251.7 by 30, we get 8.39.
Thus,
= (8.39 ± 0.1) g cm-3 = (8.4 ± 0.1) g cm-3
Below are the results for the readings for the aluminum materials:
The calculations for finding the volume and density are done in the same way as the before sample calculation shows.
The above graph shows the density graphically. If we notice then the slope of the black line is all most equal to the average of the three densities of the aluminum materials.
ρavg = = = 2.9 g cm-3
∆ ρavg = = = = 0.25 g cm-3
ρavg ± ∆ ρavg = (2.9 ± 0.25) g cm-3
Thus, the average density is equal to the gradient of the black line in the graph. The other two lines show the minimum (red line) slope of the density and the maximum (green line). It is not necessary that their average will be the slope of the black line.