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Significant figures

Discussion in 'Science' started by ScienceGuy, Feb 11, 2016.

  1. ScienceGuy

    ScienceGuy Established commenter

    My Yr 11 students recently completed an AQA certificate Physics paper with the following question.

    Calculate the terminal velocity in cm/s for the falling ball. Use the appropriate number of significant figures.

    The data required for the calculation was taken from a results table and, whilst there were other ways to calculate the answer correctly, the expected method was to divide 10 cm by 2.15 seconds.

    The answer I would have expected to receive full credit would have been 4.65 cm/s due to the number of significant figures used for time and possibly accepting 4.651 (one more decimal place than the reading used for the calculation). The only answer allowed in the markscheme for full credit was 4.7 seconds.

    Looking at the specification, there is a line about using appropriate numbers of significant figures but no detail as to what we should be teaching our students to use. Does anyone have any guidance as to either what the accepted number of significant figures would be in this case (for GCSE / AQA Certificates) and more importantly why?

    Thanks in advance
     
  2. rich_hodgetts

    rich_hodgetts New commenter

    Its a bit ambiguous in that case - typically and answer is quoted to the same SF as the numbers used to calculate it. As the number of significant figures used informs how precisely the quantity was measured this avoids introducing false accuracy into the final answer.

    In the example you quote, 2.15cm is clearly to 3 SF, 10cm could technically be 1 SF but is probably 2. To avoid adding any false accuracy then the answer should be quoted to 2 SF as this is the lowest number of sig figs for the numbers used.

    Rich
     
  3. wanet

    wanet Star commenter

    Is it simply that 10 has nothing after decimal point, 2.15 has 2 figures, this averages as 1 sig fig hence their answer.
     
  4. DonutBoy99

    DonutBoy99 New commenter

    10cm is 2 Sig figs at best, so that dictates the precision of the final answer.
    The analogy I use with students is that of a chain being only as strong as the weakest link.
     
  5. Rhysboy

    Rhysboy New commenter

    10 is 1 SF, so the answer should be give to 1 SF, which would be 5.
    If it was written as 1.0 x 10 (raised to the power 1, can't do superscript on this site), then it would be 2 SF.
    To be honest, that is not a great question.
     
  6. doctoryes

    doctoryes Occasional commenter

    I have marked GCSE Science papers. For the example that you have given I would have said that 2 sf is correct as stated by *Donutboy99*. For significant figures the zeros are counted, so 10 would be 2sf and 10.0 would be 3sf. As the question states "give the answer to an appropriate no. of sf" this means there is only one answer. If the question didn't say that, then I would say minimum 2 sf, but they wouldn't lose a mark for 3sf (or even more sf if applicable. (I don't think 1 sf would be acceptable though).
     

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