Rounding Decimals

Learning Outcomes

Round a decimal number to a given place value

In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at $\$3.279$ per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay $$3.28$ , because the final price would be rounded to the nearest cent.

Suppose we wanted to round $$2.72$ to the nearest dollar. Is it closer to $$2$ or to $$3$ ? What if we wanted to round $$2.72$ to the nearest ten cents; is it closer to $$2.70$ or to $$2.80$ ? The number lines in the image below can help us answer those questions.

(a) We see that $2.72$ is closer to $3$ than to $2$ . So, $2.72$ rounded to the nearest whole number is $3$ .

(b) We see that $2.72$ is closer to $2.70$ than $2.80$ . So we say that $2.72$ rounded to the nearest tenth is $2.7$ .

In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72.
Can we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.

Round a decimal.

Locate the given place value and mark it with an arrow.
Underline the digit to the right of the given place value.
Is this digit greater than or equal to $5 ?$
- Yes – add $1$ to the digit in the given place value.
- No – do not change the digit in the given place value
Rewrite the number, removing all digits to the right of the given place value.

Tip: If the digit to the right of your given place value is 5 or above, give your given place value a shove. If the digit to the right of your given place value is 4 or less, let your given place value rest.

example 1

Round $18.379$ to the nearest hundredth.

Show Answer

$18.379$
Locate the hundredths place and mark it with an arrow.
Underline the digit to the right of the $7$ .
Because $9$ is greater than or equal to $5$ , add $1$ to the $7$ .
Rewrite the number, deleting all digits to the right of the hundredths place.	$18.38$
$18.38$ is $18.379$ rounded to the nearest hundredth.

try it 1

example 2

Round $18.379$ to the nearest

tenth
whole number

Show Answer

1. Round $18.379$ to the nearest tenth.
$18.379$
Locate the tenths place and mark it with an arrow.
Underline the digit to the right of the tenths digit.
Because $7$ is greater than or equal to $5$ , add $1$ to the $3$ .
Rewrite the number, deleting all digits to the right of the tenths place.	$18.4$
So, $18.379$ rounded to the nearest tenth is $18.4$ .

2. Round $18.379$ to the nearest whole number.
$18.379$
Locate the ones place and mark it with an arrow.
Underline the digit to the right of the ones place.
Since $3$ is not greater than or equal to $5$ , do not add $1$ to the $8$ .
Rewrite the number, deleting all digits to the right of the ones place.	$18$
So $18.379$ rounded to the nearest whole number is $18$ .

try it 2

Watch the following video to see an example of how to round a number to several different place values.

Module 0: Review