Round numbers to the nearest whole number, tenth, hundredth, ten, hundred, thousand, decimal place, or significant figure. See the rounding digit, the deciding digit, a number-line explanation, and step-by-step math.
Enter a number and choose how you want it rounded to see the digit-by-digit decision.
Whole numbers, decimals, negative numbers, and scientific notation (such as 1.23456e6) are all accepted.
Useful for money, measurements, pack sizes, pricing, and time intervals.
Most people can leave this on Standard. These options control exact-halfway ties and directional rounding.
Rounding replaces a number with a nearby value that is easier to read, communicate, estimate, or calculate with, while keeping the result reasonably close to the original number. For example, 7.63 rounded to the nearest whole number is 8. Rounded to the nearest tenth, the same number becomes 7.6. Rounded to the nearest hundredth, it stays 7.63. The rounded answer depends entirely on the place value you are asked to keep. Rounding does not change what the original number actually was; it creates an approximation. This is why a rounded answer is often written with language such as "approximately" or "about."
The basic school rounding rule is simple: look at the digit immediately to the right of the place you are rounding. If that digit is 0, 1, 2, 3, or 4, keep the rounding digit the same. If that digit is 5, 6, 7, 8, or 9, increase the rounding digit by one. Then remove or replace the remaining digits as required by the place value.
Place value tells you what a digit represents based on where it appears in a number. Consider 12,345.6789. The digit 1 is in the ten-thousands place. The digit 2 is in the thousands place. The digit 3 is in the hundreds place. The digit 4 is in the tens place. The digit 5 is in the ones place. To the right of the decimal point, 6 is in the tenths place, 7 is in the hundredths place, 8 is in the thousandths place, and 9 is in the ten-thousandths place. You cannot round correctly until you know which place value you are supposed to keep.
To round to the nearest whole number, keep the ones digit and look at the tenths digit. Example: 7.6. The ones digit is 7. The tenths digit is 6. Because 6 is at least 5, increase the ones digit from 7 to 8. Therefore 7.6 rounded to the nearest whole number is 8.
Another example: 12.3. The tenths digit is 3. Because 3 is less than 5, keep the ones digit: 12. Therefore 12.3 rounded to the nearest whole number is 12.
A number line shows that rounding is really about choosing the closest target value. Suppose you want to round 43 to the nearest ten. The two surrounding tens are 40 and 50. Their midpoint is 45. Because 43 is below 45, it is closer to 40. Therefore 43 rounds to 40. Now consider 47. It is above the midpoint 45, so it is closer to 50. Therefore 47 rounds to 50.
The digit rule and the number-line method describe the same mathematical idea. The digit rule is faster. The number line makes the reason visible.
To round to the nearest tenth, keep the tenths digit and inspect the hundredths digit. Example: 6.74. The tenths digit is 7. The hundredths digit is 4. Because 4 is less than 5, keep 7. Result: 6.7. Now consider 6.78. The hundredths digit is 8. Since 8 is at least 5, increase the tenths digit from 7 to 8. Result: 6.8.
To round to the nearest hundredth, keep two digits after the decimal point and inspect the third. Example: 3.146. The hundredths digit is 4. The thousandths digit is 6. Because 6 is at least 5, increase 4 to 5. Result: 3.15. If the number were 3.143, the deciding digit would be 3. Because 3 is less than 5, the result would be 3.14.
To round to the nearest thousandth, keep three decimal places. Example: 2.71828. The thousandths digit is 8. The next digit is 2. Because 2 is less than 5, the 8 stays. Result: 2.718.
To round to the nearest ten, keep the tens digit and inspect the ones digit. Example: 347. The tens digit is 4. The ones digit is 7. Because 7 is at least 5, increase the tens digit from 4 to 5. Replace the ones digit with 0. Result: 350. Example: 342. The ones digit is 2. Result: 340.
To round to the nearest hundred, keep the hundreds digit and inspect the tens digit. Example: 1,462. The hundreds digit is 4. The tens digit is 6. Because 6 is at least 5, increase 4 to 5. Replace the tens and ones digits with zeros. Result: 1,500. Example: 1,432. The tens digit is 3. Result: 1,400.
Rounding to the nearest 100 means exactly the same thing as rounding to the nearest hundred. Example: 4,349. The hundreds digit is 3. The tens digit is 4. Because 4 is less than 5, the result is 4,300. Now consider 4,350. The tens digit is 5. Under standard school rounding, the hundreds digit increases. Result: 4,400. The phrase "rounding to the nearest 100" is simply another way of saying "rounding to the nearest hundred."
Keep the thousands digit and inspect the hundreds digit. Example: 27,620. The thousands digit is 7. The hundreds digit is 6. Because 6 is at least 5, increase 7 to 8. Replace the remaining digits with zeros. Result: 28,000. For 27,420, the hundreds digit is 4. Result: 27,000.
Suppose you want to round 3.46 to the nearest tenth. The surrounding tenths are 3.4 and 3.5. The midpoint is 3.45. Since 3.46 is greater than the midpoint 3.45, it is closer to 3.5. Therefore 3.46 rounds to 3.5.
Some learners understand rounding more easily after watching the number move on a number line or seeing the deciding digit highlighted. For an additional visual explanation specifically focused on rounding decimals to the nearest whole number, Math with Mr. J provides a video lesson titled "Rounding to the Nearest Whole Number with Decimals." You can watch a visual lesson on rounding to the nearest whole number as a supplementary resource alongside the explanations and original visuals on this page.
Rounding can cause a carry into the next place. Example: 9.99 rounded to the nearest tenth. The tenths digit is 9. The hundredths digit is 9. Because the deciding digit is 9, the tenths digit must increase. But 9 plus 1 creates a carry. The result is 10.0 at one-decimal-place precision. Another example: 999 rounded to the nearest hundred. The hundreds digit is 9. The tens digit is 9. Rounding causes a carry. Result: 1,000. A correct rounding calculator must handle these carries automatically, which is exactly what the exact-arithmetic engine behind this calculator does on every input.
Decimal places count digits to the right of the decimal point. Example: 3.14159265. Rounded to 2 decimal places means keep 3.14 and inspect the third decimal digit. The third digit is 1. So 3.14 stays. Rounded to 4 decimal places, keep 3.1415 and inspect 9. Because 9 is at least 5, increase the fourth retained digit from 5 to 6. Result: 3.1416.
Decimal places count positions after the decimal point. Significant figures count meaningful digits beginning with the first nonzero significant digit. Consider 0.004567. Rounded to 3 decimal places, keeping three digits after the decimal gives 0.004, and the next digit is 5. Under standard rounding, that becomes 0.005. But rounded to 3 significant figures, leading zeros do not count as significant digits. The first three significant digits are 4, 5, and 6. The next digit is 7. Round 6 up to 7. Result: 0.00457. These are completely different rounding instructions applied to the exact same number.
Significant figures communicate the precision of a number. In 4,567, all four digits are significant. In 0.004567, the leading zeros are placeholders and are not counted as significant figures. In 1,200, the number of significant figures can depend on how the value is written and what precision is intended. Scientific notation removes much of this ambiguity: 1.20×10³ clearly contains 3 significant figures. Rounding to significant figures is especially common in science, engineering, measurement, and laboratory work.
Consider 1.23456×10⁶. Rounded to 3 significant figures, keep 1.23. The next digit is 4. Because 4 is less than 5, the result is 1.23×10⁶, which equals 1,230,000. The Scientific Calculator can help with broader calculations involving scientific notation, powers, roots, logarithms, and trigonometry.
Money is commonly displayed to two decimal places because one cent is $0.01. Example: $19.987. To round to the nearest cent, keep the hundredths digit and inspect the thousandths digit, which is 7. Because 7 is at least 5, round the hundredths digit upward. Result: $19.99. However, not every financial calculation should be rounded at each intermediate step. Rounding repeatedly during a chain of calculations can create larger cumulative differences. When possible, keep sufficient internal precision and round the final displayed result according to the situation.
Suppose a measured length is 12.746 cm. Rounded to the nearest tenth, that is 12.7 cm. Rounded to the nearest hundredth, that is 12.75 cm. Rounding does not make the measurement more accurate; it changes the precision of how the value is reported. The appropriate rounding level depends on the measuring tool, the context, and how the result will be used.
Percentages often produce more decimal places than you need. Suppose a percentage calculation produces 67.485%. Rounded to one decimal place under standard rounding, that is 67.5%. The Percentage Calculator can help when you first need to determine what percent one number is of another, percentage increase, percentage decrease, or other percentage relationships.
A fraction represents division. Example: 2/3. Calculate 2 ÷ 3 = 0.666666.... Rounded to 2 decimal places, that is 0.67. Rounded to 3 decimal places, that is 0.667. The Fraction Calculator can convert fractions, simplify them, and perform fraction arithmetic.
Division can produce decimals that terminate or continue indefinitely. Example: 10 ÷ 6 = 1.666666.... If a problem asks for the answer rounded to 2 decimal places, the result is 1.67. The Long Division Calculator can show the complete Divide, Multiply, Subtract, Bring Down process and identify repeating decimals.
Negative numbers follow the same idea of choosing the nearest target value. Consider -3.4 rounded to the nearest whole number. It lies between -4 and -3. It is closer to -3. Therefore -3.4 rounds to -3. Now consider -3.6. It is closer to -4. Therefore -3.6 rounds to -4. A number line can make this much easier to understand.
Halfway values require a tie-breaking rule. For ordinary school-style rounding with positive numbers, 2.5 usually rounds to 3. This page's default Standard method explicitly uses half away from zero. Therefore 2.5 → 3 and -2.5 → -3. Other mathematical and computing systems may use other tie rules, which is why advanced rounding methods are clearly labeled here rather than silently changing your results.
Banker's rounding is another name commonly used for round half to even. If a number is exactly halfway, choose the candidate whose final retained digit is even. Examples: 2.5 → 2. 3.5 → 4. 4.5 → 4. 5.5 → 6. This reduces systematic upward bias across some very large collections of rounded values. It is not the same method most elementary school worksheets mean by "5 or more, round up."
The ceiling of a number moves toward positive infinity. Examples: ceil(4.1) = 5. ceil(-4.9) = -4. The floor moves toward negative infinity. Examples: floor(4.9) = 4. floor(-4.1) = -5. These are directional operations. They are not the same as ordinary rounding to the nearest value.
Truncation simply removes digits beyond a specified place instead of checking whether the next digit should change the retained value. Example: 4.98 truncated to one decimal place is 4.9. Ordinary rounding to one decimal place would give 5.0. For negative numbers, -4.98 truncated to one decimal place is -4.9. This is why truncation differs from floor, which would move toward negative infinity.
Sometimes the target is not a standard decimal place. For example, a store or measurement system might need values rounded to the nearest 0.05. Suppose the number is 12.37. The nearest multiples of 0.05 are 12.35 and 12.40. 12.37 is 0.02 away from 12.35 and 0.03 away from 12.40. Therefore 12.37 rounds to 12.35 to the nearest 0.05. Custom-increment rounding is useful when values must fit specific pricing increments, measurement increments, time blocks, or packaging quantities.
Every rounding operation replaces an exact or more precise number with an approximation. One small difference may be harmless, but repeated rounding can accumulate. Suppose several intermediate calculations are rounded too early. Each approximation can influence the next step. By the end, the final answer may differ noticeably from a calculation that retained full precision until the last step. A useful general rule is to keep extra precision during intermediate calculations and round the final result when possible. This is particularly important in finance, statistics, science, engineering, and repeated calculations.
Statistics such as mean, variance, standard deviation, and percentages may depend on many values. Rounding each input or intermediate result too aggressively can change the final statistic. If you are calculating descriptive statistics, use the Statistics Calculator with the original data when possible, then round the final result to the precision appropriate for your report.
Looking at the wrong digit. Always inspect the digit immediately to the right of the place being kept.
Rounding every digit one at a time. Do not repeatedly round from right to left. Use the original number and the requested place. Example: 2.449 rounded directly to the nearest tenth is 2.4. Do not first round 2.449 to 2.45 and then round that to 2.5; that is double rounding and can change the result.
Forgetting to replace whole-number digits with zeros. When rounding 4,672 to the nearest hundred, the result is 4,700, not 47.
Confusing decimal places with significant figures. They measure precision differently.
Thinking rounding changes the original value. The rounded number is an approximation.
Using ceiling or floor as though they were standard rounding. They follow directional rules, not nearest-value rules.
Misunderstanding negative numbers. Use the number line and the selected rounding method.
Rounding too early. Carry sufficient precision through intermediate calculations whenever practical.
Step 1: Identify the place value you must round to. Step 2: Locate that digit. Step 3: Look exactly one digit to its right. Step 4: Under standard rounding, 0 through 4 means keep the rounding digit; 5 through 9 means increase it by 1. Step 5: For decimal-place rounding, remove the digits to the right; for whole-number place values, replace digits to the right with zeros. Step 6: Check whether a carry occurred. Step 7: If the number is negative or exactly halfway, confirm which rounding method is being used.
Do not leave knowing only that "3.146 rounds to 3.15." Leave knowing what rounding means, and that a rounded number is an approximation. Know what place value is, and how to find the rounding digit and the deciding digit. Know how to round to the nearest whole number, tenth, hundredth, ten, hundred, and thousand, and know that nearest 100 means nearest hundred. Understand rounding on a number line, and know how to round decimals, significant figures, and the difference between significant figures and decimal places. Understand halfway values, and know that this calculator's standard method uses half away from zero. Understand ceiling, floor, and truncation, and know how negative numbers round. Know how to round money, percentages, and measurements, and understand why repeated rounding can create error. And most importantly, you can see why the Rounding Calculator produced the answer it did. That is what the CalculateThisWay Rounding Calculator should help someone understand.
| Task | What to Keep | What to Check |
|---|---|---|
| Nearest Whole | Ones | Tenths |
| Nearest Ten | Tens | Ones |
| Nearest Hundred | Hundreds | Tens |
| Nearest Thousand | Thousands | Hundreds |
| Nearest Tenth | Tenths | Hundredths |
| Nearest Hundredth | Hundredths | Thousandths |
| Nearest Thousandth | Thousandths | Ten-Thousandths |
| Method | Rule |
|---|---|
| Standard / Half Away From Zero | Halfway values move away from 0 |
| Half to Even | Halfway values go to the even retained digit |
| Half Toward Zero | Halfway values move toward 0 |
| Ceiling | Toward +infinity |
| Floor | Toward -infinity |
| Truncate | Remove extra digits toward 0 |
I already have a number and need to change its displayed precision or round it to a nearby place value.
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Open Calculator ›What is rounding?
Rounding replaces a number with a nearby value that is easier to read or work with while keeping the result reasonably close to the original number. 7.63 rounded to the nearest whole number is 8.
How do you round a number?
Find the place value you are rounding to, look one digit to the right of it, and if that digit is 5 or more increase the rounding digit by 1; if it is less than 5 keep the rounding digit the same.
What are the rounding rules?
Look at the digit immediately to the right of the place you are rounding. A deciding digit of 0 through 4 keeps the rounding digit the same. A deciding digit of 5 through 9 increases the rounding digit by 1.
What does 5 or more round up mean?
It is a shorthand for the standard rounding rule: if the digit to the right of the place you are keeping is 5, 6, 7, 8, or 9, the kept digit increases by 1.
How do I round to the nearest whole number?
Keep the ones digit and look at the tenths digit. If the tenths digit is 5 or more, increase the ones digit by 1; otherwise keep it the same. 7.6 rounds to 8.
How do I round decimals to the nearest whole number?
Look only at the first digit after the decimal point. 12.3 rounds to 12 because 3 is less than 5, and 7.6 rounds to 8 because 6 is at least 5.
How do I round to the nearest tenth?
Keep the tenths digit and look at the hundredths digit. 6.74 rounds to 6.7, and 6.75 rounds to 6.8 under standard rounding.
How do I round to the nearest hundredth?
Keep two digits after the decimal point and look at the third. 3.146 rounds to 3.15 because the thousandths digit, 6, is at least 5.
How do I round to the nearest thousandth?
Keep three digits after the decimal point and look at the fourth. 2.71828 rounds to 2.718 because the next digit, 2, is less than 5.
How do I round to the nearest ten?
Keep the tens digit and look at the ones digit. 347 rounds to 350 because the ones digit, 7, is at least 5.
How do I round to the nearest hundred?
Keep the hundreds digit and look at the tens digit, then replace the tens and ones digits with zeros. 1,462 rounds to 1,500.
How do I round to the nearest 100?
Rounding to the nearest 100 means exactly the same thing as rounding to the nearest hundred. 4,349 rounds to 4,300, and 4,350 rounds to 4,400 under standard rounding.
How do I round to the nearest thousand?
Keep the thousands digit and look at the hundreds digit, then replace the remaining digits with zeros. 27,620 rounds to 28,000.
How do you round using a number line?
Place the number between its two nearest target values and compare it to the midpoint. Whichever target value the number is closer to is the rounded answer.
How do you round decimals?
Decide which decimal place to keep, look at the digit immediately to its right, and apply the same 5-or-more rule used for whole numbers.
What is a rounding digit?
The rounding digit is the digit in the place value you are rounding to, the digit that may change.
What is the deciding digit?
The deciding digit is the digit immediately to the right of the rounding digit. It determines whether the rounding digit stays the same or increases by 1.
What is a whole number?
A whole number is a number with no fractional or decimal part, such as 0, 7, or 42.
What is a tenth?
A tenth is one of ten equal parts of a whole, written as the first digit after the decimal point, worth 0.1.
What is a hundredth?
A hundredth is one of one hundred equal parts of a whole, written as the second digit after the decimal point, worth 0.01.
What is a thousandth?
A thousandth is one of one thousand equal parts of a whole, written as the third digit after the decimal point, worth 0.001.
What happens when the deciding digit is 5?
The number is exactly halfway between two possible rounded values, so the result depends on which tie-breaking rounding method is used.
How do you round 2.5?
Under this calculator's default Standard method, half away from zero, 2.5 rounds to 3. Under half to even it rounds to 2.
How do you round -2.5?
Under Standard, half away from zero, -2.5 rounds to -3, moving away from zero the same way 2.5 rounds to 3.
How do negative numbers round?
Negative numbers round to whichever nearby target value is closest on the number line. -3.4 rounds to -3, and -3.6 rounds to -4.
What is banker's rounding?
Banker's rounding is another name for round half to even, where exact halfway values round to whichever candidate has an even final digit.
What is round half to even?
For exact halfway values, round half to even picks the nearby value whose retained digit is even. 2.5 rounds to 2, and 3.5 rounds to 4.
What is ceiling?
Ceiling rounds toward positive infinity. ceil(4.1) is 5, and ceil(-4.9) is -4.
What is floor?
Floor rounds toward negative infinity. floor(4.9) is 4, and floor(-4.1) is -5.
What is truncation?
Truncation removes digits beyond a chosen place value without checking whether the next digit would round it up. 4.98 truncated to one decimal place is 4.9.
What is the difference between floor and truncation?
Floor always moves toward negative infinity, while truncation always moves toward zero. For -4.9, floor gives -5, but truncation gives -4.
What are significant figures?
Significant figures are the meaningful digits in a number, starting from the first nonzero digit, used to communicate precision.
How do you round to significant figures?
Count significant digits starting from the first nonzero digit, keep the requested amount, and apply the standard rounding rule to the next digit. 0.004567 to 3 significant figures is 0.00457.
What is the difference between significant figures and decimal places?
Decimal places count digits after the decimal point regardless of leading zeros. Significant figures ignore leading zeros and start counting at the first nonzero digit.
How do you round scientific notation?
Round the mantissa to the requested number of significant figures and keep the same power of ten. 1.23456e6 to 3 significant figures is 1.23e6, or 1,230,000.
How do you round money?
Money is usually rounded to two decimal places, the nearest cent. $19.987 rounds to $19.99.
How do you round percentages?
Choose the number of decimal places you need and apply the standard rounding rule. 67.485% to one decimal place is 67.5%.
How do you round measurements?
Round to the precision that matches how the measurement was taken. 12.746 cm to the nearest tenth is 12.7 cm.
How do I round a fraction to a decimal?
Divide the numerator by the denominator, then round the resulting decimal. 2/3 equals 0.666666..., which rounds to 0.67 at two decimal places.
What is double rounding?
Double rounding is rounding a number in two separate steps instead of one, which can change the final answer. Round 2.449 directly to the nearest tenth, 2.4, rather than rounding it to 2.45 first.
Why should I avoid rounding too early?
Rounding intermediate results can accumulate error across a chain of calculations. It is usually best to keep extra precision until the final step.
What does rounding to the nearest 0.05 mean?
It means finding the closest multiple of 0.05 to your number. 12.37 rounded to the nearest 0.05 is 12.35.
The selected target place determines the digit retained. Standard rounding inspects the next digit to the right of that place, and the default method uses half away from zero for exact halfway cases, so 2.5 becomes 3 and -2.5 becomes -3. Advanced methods such as half to even, half toward zero, ceiling, floor, and truncation use their explicitly stated rules instead, and are only applied when you choose them under Advanced Rounding Method. Decimal places and significant figures are calculated differently: decimal places count digits after the decimal point, while significant figures count meaningful digits starting from the first nonzero digit, regardless of how many leading zeros come before it. Whole-number place rounding, such as rounding to the nearest ten, hundred, thousand, or ten thousand, replaces the lower place-value digits with zeros so the result still reflects correct place value. Custom increment rounding finds the nearest valid multiple of the requested increment, such as the nearest 0.05 or the nearest 25. Internally, this calculator parses your input as an exact decimal (including scientific notation) and performs every comparison and every carry using exact integer arithmetic rather than ordinary binary floating-point math, specifically to avoid unsafe floating-point comparisons around exact halfway cases such as 6.75, 2.5, or 12.37, values that binary floating point can otherwise store with tiny hidden errors. Display formatting preserves the requested precision where useful, so rounding 3 to two decimal places can correctly display 3.00. Rounding changes precision, not the original underlying value; this calculator does not claim infinite precision, and very long or unusual inputs are capped at a generous digit limit to keep the page responsive.
Last reviewed: September 24, 2026