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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.

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.