Identify the Two Benchmarks
When rounding 8.472 to the nearest tenth, the two possible answers are 8.4 and 8.5.
8.4 < 8.472 < 8.5
Free Math Guide
Rounding Decimals Explained
Learn how to identify the rounding place, inspect the deciding digit, choose the nearest benchmark, and round decimals accurately.
Rounding replaces a decimal with a nearby value that is easier to read, estimate, or calculate with. To round correctly, identify the requested place and inspect only the digit immediately to its right. That deciding digit tells you whether the rounding digit stays unchanged or increases by one.
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What Does It Mean to Round a Decimal?
A decimal lies between two benchmark values at the requested place. Rounding selects the benchmark that is closest to the original number.
Choose the Closer Benchmark
The midpoint between 8.4 and 8.5 is 8.45. Because 8.472 is above the midpoint, it is closer to 8.5.
8.472 ≈ 8.5
Rounding Changes the Form, Not the Estimate’s Purpose
The rounded value is not exactly equal to the original value. The symbol ≈ means “approximately equal to.” For example, 8.472 ≈ 8.5.
Rounding Places and Deciding Digits
The rounding digit is in the place named by the question. The deciding digit is always one place to its right.
| Round To | Rounding Digit | Deciding Digit | Example |
|---|---|---|---|
| Nearest whole number | Ones | Tenths | 18.67 → inspect 6 |
| Nearest tenth | Tenths | Hundredths | 7.34 → inspect 4 |
| Nearest hundredth | Hundredths | Thousandths | 5.286 → inspect 6 |
| Nearest thousandth | Thousandths | Ten-thousandths | 12.7048 → inspect 8 |
Example: Round 8.472 to the Nearest Tenth
8
.
4
7
2
4 is the rounding digit
7 is the deciding digit
Do Not Look at Every Digit to the Right
Only the digit immediately to the right makes the rounding decision. Once you identify that digit, the digits farther right do not change the rule.
Digits 0–4 Keep It; Digits 5–9 Add One
Keep the Rounding Digit
If the deciding digit is less than 5, leave the rounding digit unchanged and remove the digits to its right.
7.34 to the nearest tenth
7.34 ≈ 7.3
Increase the Rounding Digit
If the deciding digit is 5 or greater, add one to the rounding digit and remove the digits to its right.
7.38 to the nearest tenth
7.38 ≈ 7.4
Memory aid: 0, 1, 2, 3, and 4 keep the rounding digit.
5, 6, 7, 8, and 9 increase it by one.
How to Round a Decimal on a Number Line
A number line shows why the deciding-digit rule works. Place the original decimal between its two benchmark values and compare it with their midpoint.
8.472
8.4
8.45
8.5
Lower benchmark
8.4 is the lower possible rounded value.
Midpoint
8.45 is exactly halfway between 8.4 and 8.5.
Original number
8.472 is greater than 8.45, so it lies in the upper half.
Rounded value
8.472 is closer to 8.5 than 8.4, so it rounds to 8.5.
What Happens at the Exact Midpoint?
Under the standard elementary-school rounding rule, a value exactly at the midpoint rounds to the upper benchmark. Therefore, 8.45 rounds to 8.5 when rounding to the nearest tenth.
Rounding to Different Decimal Places
Round 18.67
- The ones digit is 8.
- The tenths digit is 6.
- Since 6 is at least 5, increase 8 to 9.
18.67 ≈ 19
Round 7.34
- The tenths digit is 3.
- The hundredths digit is 4.
- Since 4 is less than 5, keep the 3.
7.34 ≈ 7.3
Round 5.286
- The hundredths digit is 8.
- The thousandths digit is 6.
- Since 6 is at least 5, increase 8 to 9.
5.286 ≈ 5.29
Round 12.7048
- The thousandths digit is 4.
- The ten-thousandths digit is 8.
- Since 8 is at least 5, increase 4 to 5.
12.7048 ≈ 12.705
Regrouping While Rounding Decimals
If the deciding digit requires you to increase a 9, the 9 becomes 0 and one is carried into the place to its left. The regrouping can continue through more than one digit.
Carry Into Another Decimal Place
Round 3.796 to the nearest hundredth.
- The hundredths digit is 9.
- The thousandths digit is 6, so increase the 9.
- The 9 becomes 0 and adds one to the tenths digit.
3.796 ≈ 3.80
Carry Into the Whole Number
Round 4.996 to the nearest hundredth.
- The hundredths digit is 9.
- The thousandths digit is 6, so round up.
- Regroup through both decimal 9s into the ones place.
4.996 ≈ 5.00
Rounding Can Change Several Digits
The deciding digit still controls only one decision. The additional changes happen because adding one to a 9 requires regrouping.
When Trailing Zeros Matter
Trailing zeros do not change a decimal’s numerical value, but they can communicate the place to which the number was rounded.
Equivalent Numerical Values
5 = 5.0 = 5.00
These decimals represent the same quantity because zeros at the end do not change the value.
Different Reported Precision
4.996 ≈ 5.00
Writing 5.00 makes it clear that the original decimal was rounded to the nearest hundredth.
If a problem specifies a decimal place, include enough
trailing zeros to show that place when appropriate.
Worked Decimal Rounding Examples
Nearest Whole Number
Round 42.19 to the nearest whole number.
- The ones digit is 2.
- The tenths digit is 1.
- Since 1 is less than 5, keep the 2.
42.19 ≈ 42
Nearest Whole Number
Round 63.81 to the nearest whole number.
- The ones digit is 3.
- The tenths digit is 8.
- Since 8 is at least 5, increase 3 to 4.
63.81 ≈ 64
Nearest Tenth
Round 9.243 to the nearest tenth.
- The tenths digit is 2.
- The hundredths digit is 4.
- Keep the 2 and remove the remaining digits.
9.243 ≈ 9.2
Nearest Hundredth
Round 0.0478 to the nearest hundredth.
- The hundredths digit is 4.
- The thousandths digit is 7.
- Increase 4 to 5.
0.0478 ≈ 0.05
Round Through a 9
Round 6.195 to the nearest hundredth.
- The hundredths digit is 9.
- The thousandths digit is 5.
- Increase the 9 and regroup into the tenths place.
6.195 ≈ 6.20
Nearest Thousandth
Round 14.3287 to the nearest thousandth.
- The thousandths digit is 8.
- The ten-thousandths digit is 7.
- Increase 8 to 9.
14.3287 ≈ 14.329
Common Decimal Rounding Mistakes
Looking at the Wrong Digit
The deciding digit must be immediately to the right of the requested rounding place.
Rounding Every Digit One at a Time
Do not round from the far-right digit toward the left. Make one decision using the correct deciding digit.
Changing the Rounding Digit When the Deciding Digit Is 4
Digits 0 through 4 keep the rounding digit unchanged. Only digits 5 through 9 increase it.
Forgetting to Remove Later Digits
After making the rounding decision, digits beyond the requested decimal place are omitted.
Ignoring Regrouping Through a 9
Increasing a 9 produces 0 in that place and carries one into the place to its left.
Thinking More Decimal Digits Always Mean a Larger Number
Decimal size depends on place value, not the number of written digits. For example, 0.9 is greater than 0.87.
Dropping a Useful Trailing Zero
Although 5 and 5.00 are equal, 5.00 communicates that the value was rounded to the nearest hundredth.
How to Round Any Decimal
1. Identify the requested place
Determine whether the problem asks for the nearest whole number, tenth, hundredth, or thousandth.
2. Locate the rounding digit
Find the digit occupying the requested place.
3. Look one place right
Identify the deciding digit immediately to the right of the rounding digit.
4. Keep it or add one
Keep the rounding digit for 0–4. Increase it by one for 5–9.
5. Regroup if necessary
If the rounding digit is 9 and must increase, carry into the place to its left.
6. Write the rounded number
Remove digits beyond the requested place and include useful trailing zeros when they communicate precision.
7. Check the benchmarks
Confirm that the answer is the closer of the two possible rounded values.
Quick check: your answer should be one of the two
benchmark values surrounding the original decimal.
Practice Rounding Decimals
Round randomized decimals to the nearest whole number, tenth, hundredth, or thousandth. Use highlighted place values, benchmark numbers, an optional number line, hints, and immediate feedback.
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Interactive Rounding Practice
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