There are often situations, typically involving measurement, where it is necessary and practical to round the values that have been obtained.
Although we are familiar with rounding values to a certain number of decimal places, rounding using significant figures can be applied to all numbers, whether or not they have a decimal point.
Significant figures are the digits considered to be significant in reporting a measurement, regardless of the location of the decimal point.
Before we begin rounding to a certain number of significant figures, we have to know which digits in a number are considered significant (shown below in red).
Starting from the left of the number, the first significant digit is the first non-zero digit.
Rounding to a certain number of significant figures follows the same rounding rules as rounding to a certain number of decimal places (see the 'Rules for rounding' panel below).
Typically, we only round the final answer in a calculation. The type of rounding should always be indicated next to any value that has been rounded. For example, if a value has been rounded to $3$3 significant figures, we would write ($3$3 s.f.) next to the value.
Write $95476$95476 to $3$3 significant figures.
Think: All digits in this number are significant because they are all non-zero.
Do: Starting from the left, the first three significant figures are $954$954, but the next digit, $7$7, is greater than $5$5, so we round up to $955$955. We replace the last two digits with zeros.
|$95476$95476||$=$=||$95500$95500 ($3$3 s.f.)|
Reflect: To write $95476$95476 to $2$2 significant figures, we would keep the first two significant digits $95$95. There is no need to round up, as the next digit, $4$4, is less than $5$5. We replace the remaining three digits with zeros.
|$95476$95476||$=$=||$95000$95000 ($2$2 s.f.)|
If we had to write $95476$95476 to $1$1 significant figure, notice that the first digit is $9$9 and because the next digit is $5$5, we need to round the $9$9 up to $10$10 and replace the remaining four digits with zeros.
|$95476$95476||$=$=||$100000$100000 ($1$1 s.f.)|
Write $0.0003785$0.0003785 to $2$2 significant figures.
Think: Leading zeros are not significant, but we keep them in our answer.
Do: Starting from the left, the first two significant figures are $37$37. Because the next digit, $8$8, is greater than $5$5, we round up to $38$38 and remove the last $2$2 digits of the number.
|$0.0003785$0.0003785||$=$=||$0.00038$0.00038 ($2$2 s.f.)|
How many significant figures are there in the number $84.00$84.00?
Round off $461585$461585 to three significant figures.
Round off $0.060070047$0.060070047 to four significant figures.
solves problems involving quantity measurement, including accuracy and the choice of relevant units