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

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

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.