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.

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.

example

Round [latex]18.379[/latex] to the nearest

1. tenth
2. whole number
   Show Solution

Solution

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

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