Rule 1: when adding or subtracting numbers, the answer should be quoted to the least number of decimal places in the sum
2.40 + 3.6584 + 0.029 = 6.0874 = 6.09g remembering to round up appropriately
Rule 2: when multiplying or dividing, the answer should be quoted to the least number of significant figures in the sum
17.32 / 2.4 = 7.21667 = 7.2g
Essentially though, the only rule you need to remember is that your answer cannot be more precise than the least precise piece of information you put into the calculation.
For example, say we carry out a titration three times. The titres we record from the burette are 27.10 cm3, 27.25 cm3 and 29.40 cm3. If we average these readings (ignore that they are not all concordant titres), the answer comes to 27.916 cm3. My burette has not suddenly acquired a scale with a higher resolution – I can’t read the scale to 3 decimal places, only 2, so I have to round up. The average titre is 27.92 cm3.
The zero may be significant when rounding so pay attention, especially when using a calculator.
4.99 x 10-2 rounded to 2 significant figures is 5.0 x 10-2 NOT 5 x 10-2.
And finally, never round up until you reach the very end of your calculation otherwise you will find that your answer does not match the mark scheme.
Common mistake …. do not round up sequentially.
7.4469 rounded to 2 significant figures is 7.4.
Students often start at the far end and round up in stages e.g. 7.4469 – 7.447 – 7.45 – 7.5 (which is incorrect).
Practice questions
1. How many significant figures in the following?
(a) 2.54g
(b) 2.0070g
(c) 1.86 x 103g
2. Give the answers to each calculation to the appropriate number of significant figures
(a) 46.247g + 3.219g + 0.224g
(b) 26.6g + 0.0028g + 0.00002g
(c) 9.2g / 19.00g
(d) 0.11g x 0.0272g
Answers
1 (a) 3 (b) 5 (c) 3
2 (a) 49.690g – all masses were weighed to 3 dp
(b) 26.6g – the least precise measurement was to only 1 dp
(c) 0.48g – the least precise measurement has 2 sf
(d) 0.0030g – the least precise measurement has 2 sf so we need to round up appropriately (2 sf means the answer must be 0.0030g and NOT 0.003g)