Significant Figures

Watch the video below on significant figures.

Figure 1: The red and brown is called a counting stick and can only measure to 10 cm.

A picture containing water, clock

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Figure 2: The top part of this metre stick can read to the nearest 1 cm, the bottom to the nearest mm.

When Physicist use numbers it is usually because they have measured something. Significant figures tell us how precise our measurement.

For example a student uses a metre stick to measure the length of a jotter.

A close up of a measure

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If the student measures a jotter with the “counting stick” (in the top picture in the red and brown) which is marked in 10 cm graduations they will not be able to get a very good value. You would get that the jotter was just under 30 cm long but you wouldn’t be able to say much more.

If the student uses a ruler marked in centimetre marks they could say that the jotter was over 29 cm but less than 30 cm and closer to 30 cm than 29 cm, you’d say it was about 30 cm long.

If the jotter was measured with a metre stick marked in millimetres the jotter could be measured as 29.7 cm long

Figure 3 Here is a diagram of the jotter measured with different metre stick.

You need to look at significant figures with rounding which I will cover this week too.

30 cm is one significant figure and means a number between 25 cm and 34 cm which would be rounded to 30 cm. This is how you could record the number if you used the counting stick.

29 cm is two significant figures and means a number between 29.5 cm and 30.4 cm, which would be rounded to 29 cm. This is how you could record the number if you used the metre stick marked in cm only

29.7 cm is three significant figures and means a number between 29.65 cm and 29.74 cm, which would be rounded to 29.7 cm. This is probably the best measurement we should aim to make and to do this we would need a metre stick with millimetre graduations.

29.76 cm is four significant figures and means a number between 29.755 cm and 29.764 cm, it is unlikely that you could measure a jotter to that level of precision as the pages would vary by more than this. You would need a better piece of apparatus than a metre stick to measure this.

How many Significant Figures?

The simple rule is this: Your answer should have no more than the number of significant figures given in the question.

If different numbers in the question are given to a different number of significant figure you should use the number of significant figures in the value given to the smallest number of significant figures.

Example

Question: A rocket motor produces 4,570 N (3 sig fig) of thrust to a rocket with a mass of 7.0 kg (2 sig fig). What is the acceleration of the rocket?

The calculated answer to this question would be 652.8571429 ms-2 . However the least accurate value we are given in the question is the value of the mass. This is only given to two significant figures. Therefore our answer should also be to two significant figures: 650 ms–2 .

You might not think that this makes a difference, but during the SQA Intermediate 2 paper in 2006 Q25 was written to test significant figures.

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