How to Round to the Nearest Tenth—Step-by-Step Guide
How to Round to the Nearest Tenth
Step-by-Step Guide: Rounding to the Nearest Tenth in 3 Easy Steps
Free Step-by-Step Guide: How to round to the nearest tenth.
Learning and understanding how to round numbers is an important and useful math skill that makes working with large numbers faster and easier.
When it comes to rounding decimals, learning how to round the nearest tenth decimal place is a pretty straightforward process provided that you understand a few vocabulary terms, the meaning of place value, and some simple procedure.
This free Step-by-Step Guide on Rounding to the Nearest Tenth will teach you everything you need to know about how to round a decimal to the nearest tenth and it cover the following topics:
Now, lets begin learning how to round to the nearest tenth by recapping some important math vocabulary terms and concepts.
(Looking for help with rounding to the nearest hundredth and rounding to the nearest thousandth?)
What is rounding in math?
In math, rounding is the process of approximating that involves changing a number to a close value that is simpler and easier to work with. Rounding is done by replacing the original number with a new number that serves as a close approximation of the original number.
For example, if a new pair of basketball sneakers costs $99.88, you could use rounding to conclude that you will need $100 to purchase the sneakers. In this example, you would be rounding to the nearest whole dollar and the purpose of rounding would be to replace the actual cost of “ninety-nine dollars and eight-eighty cents” with an approximated value of “one hundred dollars,” since it is simpler and easier to work with.
Figure 01: You could use rounding to say that a pair of sneakers that actually costs $99.88 has an approximate cost of $100, since one hundred is simpler and easier to work with.
As shown in Figure 01 above, $100 is simpler and easier to work with than $99.88. So, if you had to estimate the cost of 7 pairs of basketball shoes, you could easier estimate that the cost would be $700 (since 7 x 100 = 700).
What is the significance of 5 when it comes to rounding?
The next important thing to remember when it comes to rounding is the significance of the number 5. When you first learn how to perform simple rounding, you may use a visual aid called a rounding hill as shown in Figure 02 below. A rounding hill shows how, when it comes to rounding, if whatever digit you are rounding is less than 5 (4 or less), you will round down. If whatever digit you are rounding is 5 or greater, you will round up. So, 5 is the cutoff for rounding up in any rounding scenario.
If digit to the right of the number being rounded is 4 or less → round down
If digit to the right of the number being rounded is 5 or greater → round up
For example, if you wanted to round 17 to the nearest ten, the result would be 20 since 7 is 5 or greater and you would have to round up.
17 → 7 is 5 or greater, so round up → 20
Conversely, if you wanted to round 13 to the nearest ten, the result would be 10 since 3 is 4 or less and you would have to round down.
13 → 3 is 4 or less, so round down → 10
Figure 02: The Rounding Hill illustrates the significance of 5 and how you can determine when to round up and when to round down.
What does rounding to the nearest tenth mean in terms of place value?
Now that you know what rounding is and when to round up or round down, the final concept that we need to review is place value.
In math, place value refers to the numerical value that a digit has by virtue of its position in the number.
For example, consider the number 3.57.
We can think of the number 3.57 as the sum of 3 ones, 5 tenths, and 7 hundredths.
A useful tool for visualizing place value is called a place value chart, where each place value has its own slot so you can clearly identify a given digits place value. Figure 03 below shows the number 3.57 within a place value chart, where you can clearly see that 3 is in the ones place, 5 is in the tenths place, and 7 is in the hundredths place.
Figure 03: A place value chart is a useful tool for identify each digit’s place value, especially when you are dealing with decimals.
If you want to learn how to round to the nearest tenth, then you will need to be able to correctly identify the place value of the tenths and hundredths place value, otherwise you will struggle to correctly round a decimal to the nearest tenth (more on why this is the case later on in this guide).
Keep Learning: Where is the hundredths place value in math?
Here are a few more examples of correctly identifying the tenths and hundredths decimal places:
4.12 → 1 is in the tenths decimal place and 2 is in the hundredths decimal place
52.783 → 7 is in the tenths decimal place and 8 is in the hundredths decimal place
0.3333 → 3 is in the tenths decimal place and 3 is in the hundredths decimal place
488.60 → 6 is in the tenths decimal place and 0 is in the hundredths decimal place
Figure 04: Examples of identifying the tenths and hundredths decimal place for 4.12, 52.783, 0.3333, and 488.6
How to Round to the Nearest Tenth in 3 Easy Steps
Now you are ready to work through a few examples where you have to round to the nearest tenth using our easy 3-step method, which works as follows:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
Let’s continue on to using these three steps to several practice problems.
Example #1: Round to the Nearest Tenth: 8.63
This first example is pretty simple. You are tasked with rounding to the nearest tenth the number 8.63.
Let’s go ahead and apply our 3-step method to solving this problem:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
In this case, 6 is in the tenths place value slot and 3 is in the hundredths place value slot as shown in Figure 05 below.
Figure 05: For the number 8.63, 6 is in the tenths place value slot and 3 is in the hundredths place value slot.
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
For this example, 3 is in the hundredths place value slot. Since 3 is less than 5, we will have to round down in the final step.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
As determined in step two, we will be rounding the hundredths place value digit, which is 3 in this example, down to zero. This effectively means that, when rounding to the nearest tenth, you must remove the hundredths value digit entirely and make the following conclusion:
Final Answer: 8.63 rounded to the nearest tenth is 8.6
This final result is illustrated in Figure 06 below. Now, let’s move onto a second example where you will have to round up to get your final answer.
Figure 06: Step One: Split the cubic polynomial into two groups
Example #2: Round to the Nearest Tenth: 32.87
For this next example, you can use the same 3-step approach to determine what is 32.8 rounded to the nearest tenth as follows:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
For the number 32.87, 8 is in the tenths place value slot and 7 is in the hundredths place value slot as shown in Figure 07.
Figure 07: Rounding to the nearest tenth: The first step is to identify the digits in the tenths and hundredths place value slots.
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
For the second example, 7 is in the hundredths place value slot. Since the number 7 is greater than 5, we will have to round up in the last step.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
We have already determined that finding 32.87 rounded to the nearest tenth will require rounding up. In this case, the 8 in the tenths decimal place will round up to a 9 and the hundredths decimal place will disappear.
Final Answer: 32.87 rounded to the nearest tenth is 32.9
This final answer is shown in Figure 08 below.
Figure 08: 32.87 rounded to the nearest tenth is 32.9
Example #3: Round to the Nearest Tenth: 119.308
Notice that this example includes a digit in the thousandths decimal place. While this is a larger number than the previous two examples, you can still use the 3-step process to find the value of 119.308 rounded to the nearest tenth.
Step One: Identify the value in tenths place value slot and the hundredths place value slot
In this example, for the number 119.308, 3 is in the tenths decimal place value slot, 0 is in the hundredths place value slot, and 8 is in the thousandths place value slot (although the 8 will not have any effect on how you solve this problem, and you can actually ignore it entirely and still correctly round 119.308 to the nearest tenth).
Figure 09: To find the value of 119.308 rounded to the nearest tenth, you only need to worry about the values in the tenths and hundredths place value slots (anything after that does not matter).
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
Continuing on, lets focus on the fact that 0 is in the hundredths place value slot for this third example.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
Since 0 is less than 5, we will have to round it down to—zero. And since zero is already zero, all that you have to do is make it disappear entirely and conclude that:
Final Answer: 119.308 rounded to the nearest tenth is 119.3
This final answer is shown in Figure 10 below.
Figure 10: How to round to the nearest tenth: 119.308 can be rounded to 119.3
Example #4: Round to the Nearest Tenth: 90.352
Just like the last example, 90.352 includes a digit in the thousandths decimal place. And, just like the last example, you can ignore that digit entirely and apply the same 3-step method as follows:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
The place value slots for 90.352 are as follows: 3 is in the tenths place value slot and 5 is in the hundredths place value slot. Again, you can ignore the 2 in the thousandths place value slot.
Figure 11: How to round to the nearest tenth: start by identifying the values of the tenths and hundredths place value digits
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
For the second step, our focus is on the 5 in the hundredths place value slot.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
Since 5 is equal to 5 or greater, we will have to round up. Remember that 5 is the cutoff for rounding up, so this is an example where the number just meets the requirements for rounding up instead of down.
Final Answer: 90.352 rounded to the nearest tenth is 90.4
The entire process for solving example #4 is illustrated in Figure 12 below.
Figure 12: 90.352 rounded to the nearest tenth is equal to 90.4
Example #5: Round to the Nearest Tenth: 149.96
Are you starting to get the hang of using the three-step process to round numbers to the nearest tenth? Let’s try rounding 149.96 to the nearest tenth and find out:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
For this fifth example, the digit in the tenths place value slot is 9 and the digit in the hundredths place value slot is 6, as shown in Figure 13 below.
Figure 13: The digit in the tenths place value slot is 9 and the digit in the hundredths place value slot is 6.
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
Moving on, note that the digit in the hundredths place value slot is 6, which is 5 or larger.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
Since 6 is equal to 5 or greater, we will have to round up. However, notice that the digit in the tenths place value slot is a 9, which can not be rounded up to the next digit. In this case, the 9 will become a zero and the digit that gets rounded up is the one in the ones place value slot (the number directly to the left of the decimal point).
So, when you round 149.96 to the nearest tenth, the 9 becomes a zero and the number 149 gets rounded up to the next whole number as follows:
Final Answer: 149.96 rounded to the nearest tenth equals 150.0
Figure 14: 149.96 rounded to the nearest tenth is 150.0
Example #6: Round to the Nearest Tenth: 3.0499
Now let’s work through one final example of rounding a number to the nearest tenth.
Remember that you only need to know the digits in the tenths and hundredths place value slots to round correctly, and you can ignore any additional numbers.
Step One: Identify the value in tenths place value slot and the hundredths place value slot
For this final example, the digit in the tenths place value slot is 0 and the digit in the hundredths place value slot is 4, as illustrated in Figure 15 below.
Figure 15: Remember that, when it comes to rounding to the nearest tenth, you can ignore any additional numbers that come after the digit in the thousandths decimal slot.
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
Just as we did in all of the previous examples, the second step requires you to identify the value of the hundredths place value digit. For the number 3.0499, this value is 4.
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
4, the digit in the hundredths place value slot, is less than 5, so we will be rounding down. So, the disappears and the 0 in the tenths place value slot stays a 0 since it can not be rounded down any further.
Therefore, we can conclude that:
Final Answer: 3.0499 rounded to the nearest tenth equals 3.0
Figure 16: 3.0499 rounded to the nearest tenth is 3.0
How to Round to the Nearest Tenth: Conclusion
Rounding is an important math skill that every student must learn at some point. While rounding integers is relatively simple, the process, while similar, gets trickier when decimals are involved.
This step-by-step guide focused on teaching you how to round numbers to the nearest tenth (i.e. to the nearest tenth decimal place). By using the following 3-step method, you can successfully round any number involving decimals to the nearest tenth:
Step One: Identify the value in tenths place value slot and the hundredths place value slot
Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller
Step Three: Round the value in the tenths place value slot up or down depending on the result from step two
This method will work for rounding any number to the nearest tenth. To recap, we used this method to solve the following examples where we were given a decimal number and tasked with rounding it to the nearest tenth:
8.63 → 8.6
32.87 → 32.9
119.309 → 119.3
90.352 → 90.4
149.96 → 150.0
3.0499 → 3.0
If you need more practice, we recommend working through the six practice problems in this guide again and/or working through the free rounding practice worksheets available on our free math worksheet libraries.
Keep Learning:
How to Round to the Nearest Hundredth (Step-by-Step Guide)
Continue your rounding journey by learning how to round to the nearest hundredth.