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Rounding and Significant Figures

GCSEAQA

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.

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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
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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.

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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.

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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.

GCSEAQA

Rounding and Significant Figures Example Questions

0.03 \: \text{A}
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a) 0.0034

b) 1600000

c) 0.10

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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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