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Practical Experiment Report Writing

Significant Figures

In experimental physics significant figures in a number refers to all the figures obtained by direct measurement, excluding any zeros which are used only to place the decimal point.

The number of significant figures you record implies to what level you can measure with the instrument.

If you record a length of 7 cm in your results it implies you can only read to the nearest cm on the instrument you used. A reading of 7.0 cm indicates you used a ruler with mm markings, whereas 7.00cm indicates you used a caliper device that reads to a tenth of a millimeter

e.g.
Measured value
Significant figures
5
1
5.00
3
0.123
3
3.1415 x 103
5

 

When numbers are used in calculations then the number of significant figures in the answer should be found by using an analysis of error measurements.

This is because the last significant figure tells the reader to what precision you are recording the value.

e.g.
Recorded result
Implied precision
7
implies that the value is between 6.5 and 7.5 the precision is 0.5 / 7 or 7%
7.00
implies that the value is between 6.995 and 7.005 the precision is 0.005 / 7.00 or 0.07 %

 

Therefore if we have values of 0.96 and 1.25 which are to be multiplied we are claiming the precision of each number is ;

0.5 % for 0.96 0.4% for 1.25

Hence 0.96 x 1.25 = 1.2 but this implies a precision of 4% and therefore we would be better to write 1.20.

As a general rule when multiplying or dividing numbers express your answer to the same number of significant figures as the least precise figure.

e.g. (i) 2.4 x 33.5 = 80.4

least precise figure is 2.4 with 2 significant figures and hence we write the answer as 80

e.g. (ii) 18.5 - 0.9300 = 19.892473

least precise figure is 18.5 with 3 significant figures and hence we write the answer as 19.9 (notice that when the answer is rounded off to three significant figures if the fourth figure is five or greater the third would increase by 1 but if it were four or less then it would stay the same).