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Rounding and Significant Figures
Rounding and Significant Figures Revision
Rounding and Significant Figures
Being able to round to a certain number of significant figures is a vital skill that you will use in your experimental work and in your exams.
Significant Figures
In a number, the first digit that is not a zero is the 1^{\text{st}} significant figure. For example, the 1^{\text{st}} significant figure in 0.71 is the 7. The following digits after this 1^{\text{st}} one will always be the 2^{\text{nd}} significant figure, 3^{\text{rd}} significant figure etc, even if they’re zeros. So if a question was to ask you to give a calculation to 2 significant figures, you would round the number so that there is only the 1^{\text{st}} and 2^{\text{nd}} significant figures (as well as any zeros before the 1st significant figure).
See below a list of numbers, and how they have been rounded to 2 and 3 significant figures.
| Number | To \boldsymbol{2} \: \textbf{s.f} | To \boldsymbol{3} \: \textbf{s.f} |
| 0.7134 | 0.71 | 0.713 |
| 6832 | 6800 | 6830 |
| 117 | 120 | 117 |
| 4.55 | 4.6 | 4.55 |
| 0.00489 | 0.0049 | 0.00489 |
| 56.5 | 57 | 56.5 |
| 235 600 000 | 240 000 000 | 236 000 000 |
| 0.06347 | 0.063 | 0.0635 |
It is important to always clarify how many significant figures you have rounded to in an answer. The clearest way to do this is write your answer and follow it with “to 3 s.f”, for example.
Decimal Places
You should already know how to round to decimal places, but here is a reminder in case you have forgotten.
Rounding to decimal places is different than rounding to significant figures. Rounding to decimal places means writing a number with a certain amount of numbers after the decimal point.
For example, if we wanted to round 5.3423 to 2 decimal places, it would be 5.34.
See below some different numbers rounded to 2 and 3 decimal places.
| Number | To \boldsymbol{2} \: \textbf{d.p} | To \boldsymbol{3} \: \textbf{d.p} |
| 0.7134 | 0.71 | 0.713 |
| 2.2362342 | 2.24 | 2.236 |
| 0.005 | 0.01 | 0.005 |
| 4.5537 | 4.55 | 4.554 |
| 0.0234 | 0.02 | 0.023 |
Example 1: Significant Figures
A car of mass 1200 \: \text{kg} moves with an acceleration of 3.8 \: \text{m/s}^2. Calculate the acceleration of the car and give your answer to \boldsymbol{2} significant figures.
Use the equation F = ma.
[2 marks]
F = ma = \textcolor{7cb447}{1200} \times \textcolor{2730e9}{3.8} = 4560 \: \text{N}
F = 4600 \: \text{N} to 2 s.f.
Example 2: Significant Figures
Calculate the resistance of a bulb if the current through it is 8.0 \: \text{A} and it’s potential difference is 6.5 \: \text{V}. Give your answer to \boldsymbol{2} significant figures.
Use the equation R = \dfrac{V}{I}.
[2 marks]
R = \dfrac{V}{I} = \dfrac{\textcolor{2730e9}{6.5}}{\textcolor{7cb447}{8}} = 0.8125 \: \Omega
R = 0.81 \: \Omega to 2 s.f.
Example 3: Significant Figures
A student wants to investigate the rate of photosynthesis from a piece of pondweed that is submerged in water. They counted 25 bubbles emerging from the pond weed in 1 minute. Calculate the rate of photosynthesis in bubbles per second. Give your answer to \boldsymbol{2} significant figures.
[2 marks]
\dfrac{\textcolor{00d865}{25}}{\textcolor{2730e9}{60}} = 0.4166666....
\text{Rate of Photosynthesis} = 0.42 \: \text{Bubbles per Second} to 2 s.f.
Rounding and Significant Figures Example Questions
Question 1: A student calculates the current through a component to be 0.02563 \: \text{A}. State this current to 1 significant figure.
[1 mark]
Question 2: Round the following numbers to 2 significant figures:
a) 0.00342
b) 1 646 000
c) 0.1
Question 3: A student wants to find the density of an object and calculates it to be 8.533 \: \text{kg/m}^3.
The student rounds their calculation to 8.5 \: \text{kg/m}^3. Have they rounded the number to 2 significant figures or 2 decimal places?
[1 mark]
The student has rounded the number to 2 significant figures.
8.53 would be the number rounded to 2 decimal places.
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