How to avoid losing marks with significant figures in A Level Physics exams

Understanding how to use significant figures is often ‘assumed knowledge’ not explicitly taught in A Level Physics, yet there are multiple marks to lose if you fail to use them properly!

In this article, I share with you the fail safe strategy I teach my students to ensure they never drop a mark over significant figures.

Understanding significant figures in physics: what are they, and why do we use them?

In physics, we deal with a lot of data. All data can be traced back to a measurement of something, but that measurement may have been used in calculations to produce values for quantities that cannot be measured directly. 

Significant figures show us how precise the initial measurement was based on the sensitivity of the instruments used. As scientists, we always have to assume the maximum amount of uncertainty in a measurement to make sure our results are reliable. Therefore, any values we calculate using that measurement have to be faithful to its original level of uncertainty. The answer to any calculation can only be as accurate as the least accurate data point. 

If we calculate the wavelength of a gamma ray with a measured frequency of 42.9182 10¹⁸ hertz (6 s.f.) using a value for the speed of light of 3.00 10⁸ m s^-1 (3 s.f.) then our answer can only be given to the least number of significant figures in our input data, in this case, three significant figures.

If we were to use a more precise measurement of the speed of light, then we could get a more significant figures in our answer.. 

What are the significant figure rules in physics?

• All non-zero digits are significant

  • 1234 (4 s.f.)

• Zeros between non-zero digits are significant

  • 1024 (4 s.f.)

• Zeros before non-zero digits are not significant

  • 0.0124 (3 s.f.)

• Zeros after non-zero digits without decimals are not significant

  • 1200 (2 s.f.)

• Zeros after non-zero digits with decimals are significant

  • 12.00 (4 s.f.)

How are significant figures assessed in A Level Physics exams?

Different exam boards assess the correct use of significant figures in slightly different ways, but there are some consistent rules.

• For practical based questions, you are expected to use significant figures correctly, and you will lose marks for not doing so

  • This includes reading measurements from apparatus, determining the gradient of a graph, performing calculations with raw data, and uncertainty calculations

• For non-practical based questions, you may be asked to give your answer to a specific number of significant figures, and you will lose marks for not doing so

• For non-practical based questions where you are not asked to give your answer to a specific number of significant figures, you may lose marks for not giving your final answer to an appropriate number of significant figures

  • Mark schemes may indicate the accepted number of significant figures required

  • Mark schemes may accept answers that round to the expected number of significant figures

  • An incorrectly calculated answer may still gain a mark for the correct use of significant figures

  • Final answers given to more than the expected number of significant figures may still gain any marks awarded for the correct use of significant figures

  • Final answers given to less than the expected number of significant figures will lose any marks awarded for the correct use of significant figures

AQA A Level Physics examiners will not award any marks for the correct use of significant figures if the final answer is given as a surd.

Edexcel A Level Physics examiners will only award the mark for the final answer in ‘show that’ questions if the answer is given to a greater number of significant figures than the answer given in the question.

OCR A Level Physics generally only penalises the incorrect use of significant figures once per exam paper, unless the mark scheme directs examiners to do otherwise. 

How to ensure you don’t lose marks for significant figures in your A Level Physics exams

A Level Physics questions are usually multi-part questions where you use your answer from part a) to calculate your answer to part b) and so on. To avoid compound rounding errors, always use the unrounded value from previous question parts.

During your calculation, always work with at least two more significant figures than your final answer requires. It is even better to leave the fully unrounded answer in your calculator and use that in the next step of the calculation.

Always write out your unrounded final answer to at least two more significant figures than your final answer requires, and then write out your rounded final answer, indicating the number of significant figures you have rounded to. 

If you are asked to give your answer to a specific number of significant figures, underline or highlight this in the question so you don’t forget to check back at the end of your calculation.

If in doubt about how many significant figures to use, always go with too many rather than too few (you may lose a mark for using too many, but you definitely will lose a mark for using too few!)

Helpful tips and tricks for significant figures in Physics

• Begin your calculation by listing the known quantities, noting the quantity with the fewest significant figures, as this is the number of significant figures your final answer will require

• Use the fraction button on your calculator rather than the divide button so that you can perform more steps in one calculation. This will help you avoid rounding errors

• Use the answer button on your calculator to use the last answer calculated in the next sum. This will also help you avoid rounding errors

• Use the unrounded calculated values from previous question parts in subsequent calculations to avoid rounding errors

• Present your final answer in its unrounded form (with an extra two significant figures) and then again in its rounded form, stating the number of significant figures you have rounded to

Summary

There may only be a handful of marks per exam paper for the correct use of significant figures, but those marks add up and could even mean the difference between one grade and another.

Follow the rules for significant figures, and use the tips and tricks I have given you to ensure that you don’t lose those all important marks. 

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