Rounding and Significant Figures

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.

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.