### Learning Objectives

- Round whole numbers to a determined place value

The electronics retailer, Best Buy, had [latex]1,026[/latex] brick and mortar stores open in October of [latex]2016[/latex]. Depending on how this information will be used, it might be enough to say that the company has approximately one thousand stores. The word *approximately* means that one thousand is not the exact count, but is close to the exact value.

In [latex]2017[/latex], the social network app, Facebook, reported its annual revenue as [latex]40.7[/latex] billion US dollars. This could mean they actually brought in [latex]$40,742,985,316[/latex] or [latex]$40,654,872,131[/latex]. Sometimes the detail is needed, but sometimes just an approximate value is good enough. The real estate app, Zillow, recorded a profit of [latex]1.07[/latex] billion US dollars; this is an approximate value. If you want to compare Facebook’s [latex]2017[/latex] revenue with Zillow’s [latex]2017[/latex] revenue, the precise dollars or even millions of dollars are unnecessary.

The process of approximating a number is called **rounding**. Numbers are rounded to a specific place value depending on how much accuracy is needed. Identifying the number of stores owned by Best Buy as approximately [latex]1[/latex] thousand means we rounded to the thousands place. Reporting the annual revenue of Facebook as [latex]40.7[/latex] billion US dollars means we rounded to the hundred millions place. Often the place value to which we round depends on how we will need to use the number.

Using a number line can help us visualize and understand the rounding process. Look at the number line below.

Suppose we want to round the number [latex]76[/latex] to the nearest ten. Is [latex]76[/latex] closer to [latex]70[/latex] ([latex]7[/latex] tens) or [latex]80[/latex] ([latex]8[/latex] tens) on the number line?

We can see that [latex]76[/latex] is closer to [latex]80[/latex] than to [latex]70[/latex]. So [latex]76[/latex] rounded to the nearest ten is [latex]80[/latex].

Now consider the number [latex]72[/latex]. Find [latex]72[/latex] on the number line.

We can see that [latex]72[/latex] is closer to [latex]70[/latex], so [latex]72[/latex] rounded to the nearest ten is [latex]70[/latex].

How do we round [latex]75[/latex] to the nearest ten?

Find [latex]75[/latex] on the number line.

The number [latex]75[/latex] is exactly midway between [latex]70[/latex] and [latex]80[/latex].

So that everyone rounds the same way in cases like this, mathematicians have agreed to round up to the higher number. So, [latex]75[/latex] rounded to the nearest ten is [latex]80[/latex].

Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than [latex]5[/latex], round down. If it is greater than or equal to [latex]5[/latex], round up.

So, for example, to round [latex]76[/latex] to the nearest ten, we look at the digit in the ones place.

The digit in the ones place is a [latex]6[/latex]. Because [latex]6[/latex] is greater than or equal to [latex]5[/latex], we increase the digit in the tens place by one. So the [latex]7[/latex] in the tens place becomes an [latex]8[/latex]. Now, replace any digits to the right of the [latex]8[/latex] with zeros. So, [latex]76[/latex] rounds to [latex]80[/latex].

Let’s look again at rounding [latex]72[/latex] to the nearest [latex]10[/latex]. Again, we look to the ones place.

The digit in the ones place is [latex]2[/latex]. Because [latex]2[/latex] is less than [latex]5[/latex], we keep the digit in the tens place the same and replace the digits to the right of it with zero. So [latex]72[/latex] rounded to the nearest ten is [latex]70[/latex].

### Round a whole number to a specific place value

- Locate the given place value. All digits to the left of that place value do not change.
- Underline the digit to the right of the given place value.
- Determine if this digit is 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.

- Replace all digits to the right of the given place value with zeros.

### example

Round [latex]843[/latex] to the nearest ten.

Solution

Locate the tens place. | |

Underline the digit to the right of the tens place. | |

Since [latex]3[/latex] is less than [latex]5[/latex], do not change the digit in the tens place. | |

Replace all digits to the right of the tens place with zeros. | |

Rounding [latex]843[/latex] to the nearest ten gives [latex]840[/latex]. |

### try it

### Example

Round each number to the nearest hundred:

- [latex]23,658[/latex]
- [latex]3,978[/latex]

### try it

### example

Round each number to the nearest thousand:

- [latex]147,032[/latex]
- [latex]29,504[/latex]

### try it

### TRY IT

Watch the video below for more examples of how to round whole numbers to a given place value.