Rounding to Significant Figures (Edexcel GCSE Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

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. 5 over 6

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

      • E.g. 4 pi, or square root of 3

    • 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 43.5789degree will round to 43.6degree

    • An angle of 135.211...degree will round  to 135.2°

Examiner Tips and Tricks

  • In an exam question check that you have written your answer correctly by considering if the value you have ended up with makes sense.

    • Remember the importance of zeros to indicate place value.

    • E.g. Round 2 530 457 to 3 significant figures, 253 (without the zeros) and 2 530 000 are very different sizes!

Worked Example

Round the following numbers to 3 significant figures.

(i) 345 256

(ii) 0.002 956 314

(iii) 3.997

(i) The first (non-zero) significant digit is in the hundred thousands column (3)
The third significant figure is therefore the value in the thousands column (5)

Count in thousands
Identify the numbers that it could round down to (345 000) or round up to (346 000)

Circle the digit on the right of the third significant figure (2)

345 space circle enclose 2 56

This digit is less than 5 so round down 

345 000 (3 s.f.)  

(ii) The first significant digit is in the thousandths column (2)
The third significant figure is therefore in the hundred thousandths column (5)

Count in hundred thousandths
Identify the number it could round down to (0.00295) or round up to (0.00296)

Circle the digit to the right of the third significant figure (6)

0.002 space 95 circle enclose 6 space 314

6 is greater than 5 so we need to round up

0.002 96 (3 s.f.) 

(iii) The first significant digit is in the units column (3)
The third significant figure is therefore in the hundredths column (9)

Count in hundredths
Identify the number it could round down to (3.99) or round up to (4.00)
Because the value in the tenths and hundredths columns is 9, it will affect higher place values 

Circle the digit to the right of the third significant figure (7)

3.99 circle enclose 7

This value is greater than 5 so it will round up

4.00 (3 s.f.)

The two zeros are necessary to indicate that it has been rounded to 3 significant figures

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Naomi C

Author: Naomi C

Expertise: Maths

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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