Round Whole Numbers
In 2013, the U.S. Census Bureau reported the population of the state of New York as 19,651,127 people. It might be enough to say that the population is approximately 20 million. The word approximately means that 20 million is not the exact population, but is close ...
Rounding Whole Numbers
In \(2013,\) the U.S. Census Bureau reported the population of the state of New York as \(19,651,127\) people. It might be enough to say that the population is approximately \(20\) million. The word approximately means that \(20\) 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. \(20\) million was achieved by rounding to the millions place. Had we rounded to the one hundred thousands place, we would have \(19,700,000\) as a result. Had we rounded to the ten thousands place, we would have \(19,650,000\) as a result, and so on. The place value to which we round to depends on how we need to use the number.
Using the number line can help you visualize and understand the rounding process. Look at the number line in the figure below. Suppose we want to round the number \(76\) to the nearest ten. Is \(76\) closer to \(70\) or \(80\) on the number line?
We can see that \(76\) is closer to \(80\) than to \(70.\) So \(76\) rounded to the nearest ten is \(80.\) Image credit: OpenStax Prealgebra
Now consider the number \(72.\) Find \(72\) in the figure below.
We can see that \(72\) is closer to \(70,\) so \(72\) rounded to the nearest ten is \(70.\) Image credit: OpenStax Prealgebra
How do we round \(75\) to the nearest ten. Find \(75\) in the figure below.
The number \(75\) is exactly midway between \(70\) and \(80.\) Image credit: OpenStax Prealgebra
So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, \(80.\) 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
- 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 \(5.\)
- Yes—add \(1\) 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 \(843\) 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:
- \(23,658\)
- \(3,978\)
Solution
| (a) | |
| Locate the hundreds place. | |
| The digit of the right of the hundreds place is 5. Underline the digit to the right of the hundreds place. | |
| Since 5 is greater than or equal to 5, round up by adding 1 to the digit in the hundreds place. Then replace all digits to the right of the hundreds place with zeros. |
|
| (b) | |
| Locate the hundreds place. | |
| Underline the digit to the right of the hundreds place. | |
| The digit to the right of the hundreds place is 7. Since 7 is greater than or equal to 5, round up by added 1 to the 9. Then place all digits to the right of the hundreds place with zeros. |
|
Example
Round each number to the nearest thousand:
- \(147,032\)
- \(29,504\)
Solution
| (a) | |
| Locate the thousands place. Underline the digit to the right of the thousands place. | |
| The digit to the right of the thousands place is 0. Since 0 is less than 5, we do not change the digit in the thousands place. | |
| We then replace all digits to the right of the thousands pace with zeros. |
|
| (b) | |
| Locate the thousands place. | |
| Underline the digit to the right of the thousands place. | |
| The digit to the right of the thousands place is 5. Since 5 is greater than or equal to 5, round up by adding 1 to the 9. Then replace all digits to the right of the thousands place with zeros. |
|
Notice that in part (b), when we add \(1\) thousand to the \(9\) thousands, the total is \(10\) thousands. We regroup this as \(1\) ten thousand and \(0\) thousands. We add the \(1\) ten thousand to the \(3\) ten thousands and put a \(0\) in the thousands place.
Discussion
Give an example from your everyday life where it helps to round numbers. You can share your example in the comments section below.
This lesson is part of:
Introducing Numbers