Whole Numbers: Learn It 3

Rounding Whole Numbers

In [latex]2021[/latex], the U.S. Census Bureau reported the population of the state of New York as [latex]20,114,745[/latex] people. One could say that the population is approximately [latex]20[/latex] million. The word approximately means that [latex]20[/latex] million is not the exact population, but is close to the exact value.

The process of approximating a number is called rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately [latex]20[/latex] million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number.

rounding

Rounding is a method used to shorten or simplify numbers by adjusting them to the closest specified value.

Using a number line can help you visualize and understand the rounding process. Let’s look at an example.

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

An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a dot at the value 76.

 

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.

An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a dot at the value 72.

 

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.

An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a dot at the value 75.

 

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 to the higher number, [latex]80[/latex]. 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.

How to: 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 [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.
  4. Replace all digits to the right of the given place value with zeros.

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

The number 76 with 7 being marked as being in the tens place, and the number 6 being marked as greater than 5.

 

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].

The number 76, with the number 80 below it. There is an arrow pointing towards 7 saying "add 1" and the 6 is crossed out with an arrow pointing saying "replace with 0".

 

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

The number 72 with 7 being marked as being in the tens place, and the number 2 being marked as less than 5.

 

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].

The number 72 with 70 below it. There is an arrow pointing to the 7 in 72 reading "do not add 1" and the 2 in 72 is crossed out with an arrow reading "replace with 0"
Round each number to the nearest hundred:

  1. [latex]23,658[/latex]
  2. [latex]3,978[/latex]