Learning Outcomes
- Round a decimal 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 [latex]\$3.279[/latex] per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay [latex]$3.28[/latex] , because the final price would be rounded to the nearest cent. In a lesson about whole numbers, we learned that we can round numbers to get an approximate value when the exact value is not needed.
Suppose we wanted to round [latex]$2.72[/latex] to the nearest dollar. Is it closer to [latex]$2[/latex] or to [latex]$3[/latex]? What if we wanted to round [latex]$2.72[/latex] to the nearest ten cents; is it closer to [latex]$2.70[/latex] or to [latex]$2.80[/latex]? The number lines in the image below can help us answer those questions.
(a) We see that [latex]2.72[/latex] is closer to [latex]3[/latex] than to [latex]2[/latex]. So, [latex]2.72[/latex] rounded to the nearest whole number is [latex]3[/latex].
(b) We see that [latex]2.72[/latex] is closer to [latex]2.70[/latex] than [latex]2.80[/latex]. So we say that [latex]2.72[/latex] rounded to the nearest tenth is [latex]2.7[/latex].
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 [latex]5?[/latex]
- Yes – add [latex]1[/latex] 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
Round [latex]18.379[/latex] to the nearest hundredth.
Solution
[latex]18.379[/latex] | |
Locate the hundredths place and mark it with an arrow. | |
Underline the digit to the right of the [latex]7[/latex]. | |
Because [latex]9[/latex] is greater than or equal to [latex]5[/latex], add [latex]1[/latex] to the [latex]7[/latex]. | |
Rewrite the number, deleting all digits to the right of the hundredths place. | [latex]18.38[/latex] |
[latex]18.38[/latex] is [latex]18.379[/latex] rounded to the nearest hundredth. |
try it
example
Round [latex]18.379[/latex] to the nearest
- tenth
- whole number
Show Solution
try it
Watch the following video to see an example of how to round a number to several different place values.