Rounding-To-Significant-Figures Aqa Foundation

Rounding to significant figures

How do I round a number to a given significant figure?

• To find the first significant figure when reading from left to right, find the biggest place value that has a non-zero digit

  • The first significant figure of 3097 is 3

  • The first significant figure of 0.006207 is 6

    • The zeros before the 6 are not significant

    • The zero after the 6 is significant

• Count along to the right from the first significant figure to identify the position of the required significant figure 

  • Do count zeros that are between other non-zero digits

    • E.g. 0 is the second significant figure of 3097

    • 9 is the third significant figure of 3097

• Use the normal rules for rounding

  • Count in units determined by the place value of the significant figure

    • If the second significant figure is in the 10’s column, count in 10’s

  • Identify numbers it could be rounded up or down to

  • Circle the number to the right of the significant figure

  • Use this value to determine which number it rounds to

• For large numbers, complete places up to the decimal point with zeros

  • E.g. 34 568 to 2 significant figures is 35 000

• For decimals, complete places between the decimal point and the first significant figure with zeros

  • E.g. 0.003 435 to 3 significant figures is 0.003 44

How do I know what degree of accuracy to give my answer to?

• If a question requires your answer to be an exact value

  • You can leave it as a simplified fraction

    • E.g.

  • You can leave it in terms of or a square root

    • E.g. , or

  • If it is an exact decimal up to and including 5 s.f., you can write it out without rounding it

    • E.g. 0.9375, or 850.25

• If the answer is not exact, an exam question will often state the required degree of accuracy for an answer

  • E.g. Give your answer to 2 significant figures

• If the degree of accuracy is not asked for, use 3 significant figures 

  • All working and the final answer should show values correct to at least 4 significant figures

  • The final answer should then be rounded to 3 significant figures

• In money calculations, unless the required degree of accuracy is stated in the question, you can look at the context

  • Round to 2 decimal places

    • E.g. $64.749214 will round to $64.75

  • Or to the nearest whole number, if this seems sensible (for example, other values are whole numbers)

    • $246 029.8567 rounds to $246 030

• When calculating angles, all values should be given correctly to 1 decimal place

  • An angle of 43.5789 will round to 43.6

  • An angle of 135.211… will round to 135.2°