## Rounding Whole Numbers

### Learning Objectives

• Round whole numbers to a determined place value The electronics retailer, Best Buy, had $1,026$ brick and mortar stores open in October of $2016$. 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 $2017$, the social network app, Facebook, reported its annual revenue as $40.7$ billion US dollars. This could mean they actually brought in $40,742,985,316$ or $40,654,872,131$. Sometimes the detail is needed, but sometimes just an approximate value is good enough. The real estate app, Zillow, recorded a profit of $1.07$ billion US dollars; this is an approximate value. If you want to compare Facebook’s $2017$ revenue with Zillow’s $2017$ 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 $1$ thousand means we rounded to the thousands place. Reporting the annual revenue of Facebook as $40.7$ 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 $76$ to the nearest ten. Is $76$ closer to $70$ ($7$ tens) or $80$ ($8$ tens) on the number line?

We can see that $76$ is closer to $80$ than to $70$. So $76$ rounded to the nearest ten is $80$. Now consider the number $72$. Find $72$ on the number line.

We can see that $72$ is closer to $70$, so $72$ rounded to the nearest ten is $70$. How do we round $75$ to the nearest ten?

Find $75$ on the number line.

The number $75$ is exactly midway between $70$ and $80$. So that everyone rounds the same way in cases like this, mathematicians have agreed to round up to the higher number. So, $75$ rounded to the nearest ten is $80$.

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 $5$, round down. If it is greater than or equal to $5$, round up.

So, for example, to round $76$ to the nearest ten, we look at the digit in the ones place. The digit in the ones place is a $6$. Because $6$ is greater than or equal to $5$, we increase the digit in the tens place by one. So the $7$ in the tens place becomes an $8$. Now, replace any digits to the right of the $8$ with zeros. So, $76$ rounds to $80$. Let’s look again at rounding $72$ to the nearest $10$. Again, we look to the ones place. The digit in the ones place is $2$. Because $2$ is less than $5$, we keep the digit in the tens place the same and replace the digits to the right of it with zero. So $72$ rounded to the nearest ten is $70$. ### Round a whole number to a specific place value

1. Locate the given place value. All digits to the left of that place value do not change.
2. Underline the digit to the right of the given place value.
3. Determine if this digit is 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.
4. Replace all digits to the right of the given place value with zeros.

### example

Round $843$ to the nearest ten.

Solution

 Locate the tens place. Underline the digit to the right of the tens place. Since $3$ is less than $5$, do not change the digit in the tens place. Replace all digits to the right of the tens place with zeros. Rounding $843$ to the nearest ten gives $840$.

### Example

Round each number to the nearest hundred:

1. $23,658$
2. $3,978$

### example

Round each number to the nearest thousand:

1. $147,032$
2. $29,504$

### TRY IT

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

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