Significant Figures

This is part of the HSC Chemistry course under Working Scientifically. 

Rules for Reporting Significant Figures

        Understanding Significant Figures in Science

        When solving calculation-based questions in science, it is not enough to just report the answer that is computed, the numbers also need to be expressed with the correct level of precision. 

        Significant figures are a way of expressing the precision of a number. Just as decimal places help us to report more accurate measurements, significant figures help us to quantify the accuracy of the measurement. The more significant figures a number has, the more precisely the value has been measured or calculated. 

         

        Rules for Counting Significant Figures 

        1. Rule 1: All non-zero digits are significant 

          Example: 

          36.7 `\rightarrow` All three digits are non-zero digits

          Number of significant figures: 3 (written as 3 s.f.) 


        2. Rule 2: Zeroes between non-zero digits are significant 

          Example: 

          2002 `\rightarrow` Both zeroes in the number are between 2's which are non-zero digits

          Number of significant figures: 4 (written as 4 s.f.) 


        3. Rule 3: Trailing zeroes without a decimal point are not significant

          Example:

          306490000 `\rightarrow` Only the zeroes between 6 and 4 are significant since the zeroes after 9 are all trailing

          Number of significant figures: 5

          *note: Adding a decimal point after the trailing zeroes makes them significant

          306490000. `\rightarrow` Since there is a decimal point at the end, all trailing zeroes are significant. 

          Number of significant figures: 9


        4. Rule 4: Leading zeroes in decimal numbers are not significant

          Example: 

          0.006606 `\rightarrow` The first three zeroes are leading in a decimal number, thus they are just placeholders

          Number of significant figures:  4 (6, 6, 0, 6) 


        Significant Figures in Calculations

        Significant figure rules also apply when performing operations like multiplication, division, addition, and subtraction 


        Multiplication & Division:

        • Rule: The answer must have the same number of significant figures as the value with the fewest significant figures, 

        Example: 

        3.742 `\times` 0.41 = 0.15

        • 3.742 has 4 sig figs
        • 0.41 has 2 sig figs `\rightarrow` Final answer must have 2 sig figs. 

         

        Addition & Subtraction:

        • Rule: The answer must have the same number of decimal places as the number with the fewest decimal places.

        Example: 

        4.1 – 3.817 = 0.3

        • 4.1 has 1 decimal place
        • 3.817 has 3 decimal places `\rightarrow` Final answer must have 1 decimal place

         

        Worked Example 1 (More Detailed Explanations in Video) 

         

        $$(4.362 + 3.1) \times 2.45$$

         

        $$= (7.462 \text{ (7.5 to 2 d.ps))} \times 2.45$$


        $$7.5 \times 2.45 = 18.2819$$

         

        $$= 18 \text{ (2 s.f.)}$$

         

         


        Worked Example 2 (More Detailed Explanations in Video 

         

        $$4.362 + 3.1 \times 2.45$$

         

        $$= 4.362 + 7.595 \text{ (7.6 to 2 s.f.))}$$

         

        $$= 11.957$$

         

        $$= 12.0 \text { (1 d.ps))}$$

         

         

        Summary: 

        Situation

        Rule

        Counting sig figs

        Use the 4 rules above (non-zeros, zeros between, etc

        Multiplication & division

        Match the value with the least number of significant figures in the question

        Addition & subtraction

        Match the value with the least number of decimal places

         


        RETURN TO WORKING SCIENTIFICALLY