# Rounding and Significant Figures

GCSEAQA

## 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.

GCSEAQA

## 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 $\boldsymbol{3} \: \textbf{d.p}$ $0.7134$ $0.71$ $0.713$ $2.2362342$ $2.24$ $2.236$ $0.005$ $0.01$ $0.005$ $4.5537$ $4.55$ $4.554$ $0.0234$ $0.02$ $0.023$
GCSEAQA

## 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.

GCSEAQA

## 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.

GCSEAQA

## 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

$0.03 \: \text{A}$

Gold Standard Education

a) $0.0034$

b) $1600000$

c) $0.10$

The student has rounded the number to $2$ significant figures.
$8.53$ would be the number rounded to $2$ decimal places.