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Using a Ruler

Measure the dimensions of a sheet of A4 paper, using a ruler marked in mm.


Width (w) = ______ mm ______ mm = ______ mm ______%

Length () = ______ mm ______ mm = ______ mm _______%

We are therefore saying that the dimensions are in the following ranges

__________ mm < w < __________ mm

__________ mm < < __________ mm

Now use the minimum and maximum values of w and   to calculate the minimum and maximum values of the surface area of a sheet of A4 paper

____________ mm2 < area < ____________ mm2

so we have (indirectly) measured the area to be

area = ____________ mm2 __________ mm2

which could be expressed as

area = ____________ mm2 ________%

Notice that the indeterminacy (uncertainty) in the area is a greater percentage of the result than the indeterminacies in the original measurements of w and .
If you have done your calculations correctly, you should find that

% indeterminacy in area = % indeterminacy in w + % indeterminacy in

2. Using a Voltmeter
Take a battery and measure its voltage using a) the 30V calibration and b) the 75V calibration.


Scale reading = ______ ____ so, voltage = ______V ______V

This means that we have found

________ V < voltage of battery < ________ V


Scale reading = ______ ____ so, voltage = ______ V _____ V

This means that we now have a smaller range of possible voltages

________ V < voltage of battery < ________ V





Reading Analogue Voltmeters

There is a choice of six different calibrations on the voltmeters.

The number written under each red terminal tells you the maximum voltage which can be measured when using that terminal.

For example, using the 30V red terminal, you can measure voltages between zero and 30V. In other words, the highest number on the scale (150) represents 30V. So, to convert scale reading to voltages, simply divide by 5 (150/30).

Similarly, if you are using the 75V calibration, divide the scale readings by 20 (150/75).

N.B. Use the mirror near the scale to help you find the correct position from which to view the scale.

c) Try using a number of different voltmeters to measure the voltage of the same battery.
Voltmeter Scale Reading Voltage /V
These results suggest that the voltmeters used are reliable/unreliable.
3. Using Vernier Callipers
a) Use a Vernier calliper to measure the thickness of a sheet of paper.

Thickness of one sheet of paper = _________ mm _______ mm

which corresponds to a % uncertainty of about ________ %

b) Now use the same Vernier calliper to find the average thickness of a sheet of paper with much greater precision.

Total thickness of _____ sheets of paper = _______ mm ____ mm

Therefore, we can say that the average thickness of one sheet of paper is ________ mm _______ mm which corresponds to a % uncertainty of about ________ %.

c) Measure the diameter of a cylindrical object at 5 different places.


____________ mm __________ mm


____________ mm __________ mm


____________ mm __________ mm


____________ mm __________ mm


____________ mm __________ mm

average diameter ____________ mm __________ mm

maximum reading ____________ mm __________ mm

minimum reading ____________ mm __________ mm

Our measurements suggest that the manufacturers have produced cylinders with a diameter given by
average diameter (maximum reading - minimum reading), which gives

____________ mm __________ mm

or, as a percentage

____________ mm __________ mm

Manufacturers often describe this percentage figure as the "tolerance" of the manufacturing process.

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