Significant figures - St. Brendan's Sixth Form College



STBRN A-level Physics

Significant figures and uncertainty

A number that represents a physical measurement does more than give a value of quantity. It gives an indication of the precision of the value.

A person measures a coin using different measuring devices. Their results are:

(i) 2.4 cm using a ruler

(ii) 2.38 cm using Vernier callipers

(iii) 2.377 cm using a micrometer.

In each case the person measured the coin as accurately as they could. The results show the certainty of the measurement.

With the ruler the person is certain of the 2 cm value but is uncertain of the “4”. A significant figure is one that has some significance but is not certain.

The Vernier callipers increase the certainty to 3 significant figures and the micrometer increases this further to 4 sf.

It would have been wrong for the person to have written 2.400 cm for the measurement with the ruler. This would have implied that the only uncertain figure was the last “0”. This is not possible with a simple ruler.

Incorporating uncertainty in writing measurements from experiments

The data above would have been clearer if the person had written:

(i) 2.4 ± 0.1 cm for the use of the ruler

(ii) 2.38 ± 0.01 cm using the Vernier callipers

(iii) 2.377 ± 0.001 cm using a micrometer.

Writing the absolute error after each reading shows the uncertainty for each measuring device. If the absolute error is displayed then any confusion posed by zeros are reduced. Zeros are used to locate the position of a decimal point as well as being values in their own right. The zero is significant if it does more than just fill the space to the decimal point.

Rules for writing answers to questions.

The rules when dealing with significant figures are :

(i) when multiplying and dividing the result has the same number of significant figures as the

least precise piece of data.

(ii) when adding or subtracting the result has the same number of decimal places as the least precise piece of data.

(iii) express the answer to addition and subtraction questions as a value ± the sum of the individual absolute uncertainties.

(iv) express the answer to division , multiplication, powers etc as the sum of the percentage uncertainties for each value.

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