Rounding: Decimal places and significant figures

In a nutshell

Rounding numbers is very useful when tasked with presenting information clearly and simply. There are two ways to round numbers: decimal places and significant figures.

Decimal places

To round a number to a certain amount of decimal places, follow this procedure.

procedure

1.	Go to the digit on the specified decimal place. Underline this digit.
2.	Circle the digit to the right of this number.
3.	If the circled digit is between $5$ and $9$ , then add $1$ to the underlined digit. If the circled digit is between $0$ and $4$ , then don't change the underlined digit.
4.	Rewrite the number, ignoring everything past the underlined digit.

Note: If you have to add $1$ to the underlined digit, and the underlined digit is a $9$ , then add $1$ to the digit to the left of the underlined digit and write the underlined digit as $0$ .

Example 1

Round $3.089$ to two decimal places.

Underline the second digit after the decimal point and circle the number to the right. In this case, underline $8$ and circle $9$ :

$3.0\underline{8}\raisebox{.5pt}{\textcircled{\raisebox{-.6pt} {9}}}$

The circled digit is greater than $4$ , .so increase the underlined digit by $1$ :

$3.0\underline{9}\raisebox{.5pt}{\textcircled{\raisebox{-.6pt} {9}}}$

Rewrite the number ignoring everything past the underlined $9$ :

$3.09$

Therefore, $3.089$ to two decimal places is $\underline{3.09}$ .

Significant figures

To round a number to a certain amount of significant figures, follow this procedure.

procedure

1.	Starting from the left, go to the $n^{th}$ digit, where $n$ is the number of significant figures. If the number is a decimal between $0$ and $1$ , then start counting only when you reached the first non-zero digit.
2.	Underline this digit and circle the digit to the right.
3.	If the circled digit is between $5$ and $9$ , add $1$ to the underlined digit. Otherwise, leave the digit unchanged.
4.	Rewrite the number, changing every digit to the right of the underlined digit to a zero and ignoring decimals (if any).

Note: The same rule applies for significant figures if the underlined digit is a $9$ and needs to be increased by $1$ .

Example 2

What is $184732.58$ when rounded to two significant figures?

First, underline the second digit from the left and circle the third digit. In this case, underline $8$ and circle $4$ :

$1\underline{8}\raisebox{.5pt}{\textcircled{\raisebox{-.6pt} {4}}}732.58$

The circled digit is less than $5$ , so don't change the underlined digit. Rewrite the number, changing every digit to the right of $8$ to a zero, and ignoring the decimals:

$180000$

Therefore, $184732.58$ rounded to two significant figures is $\underline{180000}$ .

Example 3

What is $0.003097232$ to three significant figures?

First, underline the third digit from the left, but start counting from the first non-zero digit, which is $3$ . In this case, underline $9$ and circle $7$ .

$0.0030\underline{9}\raisebox{.5pt}{\textcircled{\raisebox{-.6pt} {7}}}232$

The circled digit is greater than $4$ , so increase the underlined digit by $1$ . However, the underlined digit is $9$ , so increase the number to the left by $1$ and write $9$ as $0$ :

$0.0031\underline{0}\raisebox{.5pt}{\textcircled{\raisebox{-.6pt} {7}}}232$

Rewrite the number, ignoring any decimals to the right of the underlined digit:

$0.00310$

Therefore, $0.003097232$ rounded to three significant figures is $\underline{0.00310}$ .

Note: You can see in this example that the zero on the end of the number counts as a significant figure. $0.0031$ would not be the correct answer, as this is only given to two significant figures.