### Learning Outcomes

- Round decimals

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

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]. |