Determining the Range of Uncertainty
1) Analogue scales (rulers,thermometers meters with needles)
± half of the smallest division
2) Digital scales
± the smallest division on the readout
If the digital scale reads 5.052g, then the uncertainty would be ± 0.001g
10
40
30
20
50
Since the smallest division on the cylinder is 10 ml, the reading would be 32 ± 5 ml
Absolute Uncertainty- has units of the measurement
Absolute vs % UncertaintyAbsolute Uncertainty 0.25 ± 0.005 g 100.00 ± 0.05 g
Absolute Uncertainty
%05.0100100
05.0
%210025.0
005.0
100tmeasuremen
yuncertaint absoluteyuncertaint percentage
%
%
=xΔ
=xΔ
=
Or we can write
0.25 g ± 2 % --------- Larger % Uncertainty ------ Less Precise
100.00 g ± 0.05 % --------- Smaller % Uncertainty ------ More Precise
Addition / Subtraction of Uncertainties
● The type of uncertainty seen so far is an absolute uncertainty.– This is often written as Δx if the measurement is x
• If we add or subtract two physical quantities, their maximum uncertainties must be added together
The mass of block of metal is (11.5 ± 0.5) kg and its volume is (1000 ± 20) cm3. How would you express the density of the metal?
The dimensions of a box are recorded as follows:
Length, l = (5.0 ± 0.2) cm ,Width, b = (4.0 ± 0.1) cm, Height, h = (8.0 ± 0.2) cm
What is the maximum percentage error for the volume of the box?
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