Round to decimal places, significant figures or the nearest multiple — with seven rounding methods and exact arithmetic.
To round a number, look at the digit immediately after the place you are keeping. If it is 5 or more, round the kept digit up; if it is 4 or less, leave it as it is. So 3.14159 to two decimal places is 3.14, because the next digit is 1. Enter a number below, choose decimal places, significant figures or nearest multiple, and the calculator applies your chosen rounding method instantly.
Any number, positive or negative. Commas and spaces are ignored.
| Every method | Result |
|---|
Rounding replaces a number with a nearby, simpler value that is easier to read, write or work with. You lose a little precision and gain a lot of clarity — which is why a shop shows $19.99 rather than $19.9873, and a weather report says 23°C rather than 22.8461°C.
Every rounding job needs two decisions: where to round (which place value you are keeping) and how to handle a digit that sits exactly halfway. This calculator lets you set both.
Decimal places. Here x is your number and d is how many decimals you want to keep. Multiplying by 10d shifts the cut point to the units position, you round there, then shift back. Rounding 3.14159 to 2 places: 3.14159 × 100 = 314.159 → 314 → ÷ 100 = 3.14.
Nearest multiple. Here m is the step size — 5, 10, 0.25, anything. Dividing by m counts how many steps fit, rounding gives a whole number of steps, and multiplying back lands you on a multiple. Rounding 178 to the nearest 5: 178 ÷ 5 = 35.6 → 36 → × 5 = 180.
Significant figures. These count from the first non-zero digit rather than from the decimal point, so the rounding position depends on the size of the number. That is why 4876 to 3 significant figures is 4880, while 0.004876 to 3 significant figures is 0.00488.
Type your number, pick whether you are rounding to decimal places, significant figures or the nearest multiple, then set the amount. Preset buttons cover the common jobs — nearest whole number, tenth, hundredth, 10, 100, 1,000, million, and money to the nearest cent. Choose a method if you need something other than standard rounding, then press Round or the Enter key. The results panel shows your answer, every other method for comparison, the working, and a short history of your recent calculations.
The first three decide what happens on an exact tie such as 2.5. The last four always go the same direction, tie or not.
| Method | Rule | 2.5 → 0 dp | −2.5 → 0 dp | Typical use |
|---|---|---|---|---|
| Half up (standard) | Ties go away from zero | 3 | −3 | School maths, everyday rounding |
| Half down | Ties go toward zero | 2 | −2 | Conservative estimates |
| Half to even (banker's) | Ties go to the nearest even digit | 2 | −2 | Finance, statistics, IEEE 754 |
| Away from zero | Always increases the magnitude | 3 | −3 | Safety margins, material ordering |
| Toward zero (truncate) | Simply drops the extra digits | 2 | −2 | Computing, integer division |
| Ceiling (toward +∞) | Always goes up the number line | 3 | −2 | Pricing, capacity planning |
| Floor (toward −∞) | Always goes down the number line | 2 | −3 | Age, completed units |
Watch the negative column — it is where the methods separate. Ceiling takes −2.5 up to −2, while away-from-zero takes it out to −3. They agree on positive numbers and disagree on negative ones, which is a common source of quiet errors.
4.7 → 5 Nearest tenth: 4.74 → 4.74.746 → 4.75 Nearest thousandth: 4.7463 → 4.7464567 → 4570 2 sig figs: 0.004567 → 0.0046178 → 180 Nearest 100: 1234 → 120045,678 → 46,000 Nearest cent: $4.567 → $4.577.3 → 7.25 Nearest half: 7.3 → 7.5
| Feature | Decimal places | Significant figures |
|---|---|---|
| Counted from | The decimal point | The first non-zero digit |
| 0.004567 to 3 | 0.005 | 0.00457 |
| 4567 to 3 | 4567.000 | 4570 |
| Leading zeros | Counted as places | Never significant |
| Best for | Money and fixed units | Measurements and science |
| Round to | Setting | Example |
|---|---|---|
| Nearest whole number | 0 decimal places | 4.7 → 5 |
| Nearest tenth | 1 decimal place | 4.74 → 4.7 |
| Nearest hundredth | 2 decimal places | 4.746 → 4.75 |
| Nearest thousandth | 3 decimal places | 4.7463 → 4.746 |
| Nearest cent | 2 decimal places | $4.567 → $4.57 |
| Nearest dollar | 0 decimal places | $4.67 → $5 |
| Nearest 10 | Multiple of 10 | 178 → 180 |
| Nearest 100 | Multiple of 100 | 1234 → 1200 |
| Nearest 1,000 | Multiple of 1000 | 45,678 → 46,000 |
| Nearest million | Multiple of 1000000 | 7,499,000 → 7,000,000 |
| Nearest quarter | Multiple of 0.25 | 7.3 → 7.25 |
| Nearest eighth | Multiple of 0.125 | 7.3 → 7.25 |
Money is normally rounded to two decimal places, because that is the smallest unit most currencies use. Australian cash transactions add a second step: since 1c and 2c coins were withdrawn, cash totals are rounded to the nearest 5 cents, while card payments stay exact to the cent. You can reproduce that with the nearest multiple option set to 0.05.
In accounting, round only the final figure. Rounding each line first and then adding is what produces those frustrating one-cent discrepancies at the bottom of an invoice.
Money is where rounding rules matter most, because small differences repeat across thousands of transactions.
| Situation | Rule | Example |
|---|---|---|
| Card or bank payment | Nearest cent (2 dp) | $12.3449 → $12.34 |
| Australian cash payment | Nearest 5 cents | $12.34 → $12.35 |
| GST on a price | Nearest cent, per the ATO | $99 ÷ 11 = $9.00 GST |
| Adding GST | Multiply by 1.1, then round | $45.45 × 1.1 = $49.995 → $50.00 |
| Tax return figures | Whole dollars | $1,234.67 → $1,235 |
| Interest calculations | Full precision, round at the end | Round only the final balance |
| Share prices | Often 3–4 dp | $1.2345 stays as quoted |
Working out GST. Australian GST is 10%, so a GST-inclusive price divided by 11 gives the GST portion. For a $99 item that is exactly $9.00. Going the other way, multiply the GST-exclusive price by 1.1. Rounding to the nearest cent at the final step keeps the invoice consistent.
The five-cent rounding rule. Since 1c and 2c coins were withdrawn from circulation, Australian cash totals round to the nearest 5 cents: totals ending in 1, 2, 6 or 7 cents round down, and 3, 4, 8 or 9 cents round up. Card payments are unaffected and stay exact to the cent. Set the calculator to nearest multiple of 0.05 to reproduce this.
This is general information about how rounding works, not financial or tax advice — check current ATO guidance for your own circumstances.
Negative numbers are where methods diverge. For −4.55 rounded to 1 decimal place, half up gives −4.6 (away from zero), while ceiling gives −4.5 (up the number line). Neither is wrong — they answer different questions. Ask yourself whether you want the larger magnitude or the larger value, then pick the method that matches.
Accounting and banking. Totals are rounded to the cent, and banker's rounding is often preferred because always rounding ties up would slowly inflate large batches of figures.
Engineering and construction. Measurements are rounded to the tolerance the job allows, and material quantities are usually rounded up so you do not run short.
Science. Results are reported to the significant figures the instrument can justify — writing more digits than you measured overstates your accuracy.
Statistics. Percentages rounded individually can add to 99% or 101%, which is why published tables often carry a note explaining the difference.
Manufacturing. Parts are cut to a set precision, and rounding the wrong way on a tolerance can turn a good part into scrap.
Education. Rounding is one of the first places students meet the idea that an answer can be useful without being exact.
1) 6.5 2) 13 3) 3,500 4) 0.08 5) $8.44
1) 0.00498 2) −8 3) 6 and 8 (both go to the even digit) 4) 13.75 5) 2,000,000
What is rounding?
Rounding replaces a number with a nearby simpler value that is easier to read or use. You give up a little precision in exchange for clarity, such as writing 23 degrees instead of 22.8461 degrees.
How do you round numbers?
Look at the digit immediately after the place you are keeping. If it is 5 or more, round the kept digit up. If it is 4 or less, leave it unchanged. So 3.14159 to two decimal places is 3.14.
How do you round to two decimal places?
Keep two digits after the decimal point and look at the third. If the third digit is 5 or more, add one to the second digit. For example, 4.567 becomes 4.57 and 4.564 becomes 4.56.
How do you round to the nearest tenth?
Rounding to the nearest tenth means keeping one decimal place. Look at the hundredths digit: 4.74 becomes 4.7, while 4.76 becomes 4.8.
How do you round to the nearest whole number?
Look at the first digit after the decimal point. If it is 5 or more, round up to the next whole number; otherwise keep the whole number you have. So 4.7 becomes 5 and 4.3 becomes 4.
What are significant figures?
Significant figures are the meaningful digits in a number, counted from the first non-zero digit. In 0.004567 the leading zeros are not significant, so the first three significant figures are 4, 5 and 6.
What is the difference between decimal places and significant figures?
Decimal places are counted from the decimal point, while significant figures are counted from the first non-zero digit. 0.004567 is 0.005 to three decimal places but 0.00457 to three significant figures.
What is bankers rounding?
Bankers rounding, also called round half to even, sends an exact tie to the nearest even digit instead of always upward. So 2.5 becomes 2 and 3.5 becomes 4. It is used in finance and in the IEEE 754 computing standard because it avoids a steady upward bias.
What is the difference between rounding and truncation?
Rounding looks at the following digit and may increase the kept digit, while truncation simply deletes the extra digits. Truncating 3.19 to one decimal place gives 3.1, but rounding gives 3.2.
How do you round negative numbers?
It depends on the method. Half up sends ties away from zero, so minus 2.5 becomes minus 3. Ceiling moves up the number line instead, so minus 2.5 becomes minus 2. Choose the method that matches what you need.
How do you round money?
Money is normally rounded to two decimal places, the nearest cent. In Australia, cash totals are also rounded to the nearest 5 cents because 1c and 2c coins are no longer in circulation, while card payments remain exact to the cent.
How do you round to the nearest multiple?
Divide the number by the multiple, round the result to a whole number, then multiply back. To round 178 to the nearest 5: 178 divided by 5 is 35.6, which rounds to 36, and 36 times 5 is 180.
Why does 1.005 sometimes round to 1.00 instead of 1.01?
Because computers store 1.005 in binary as slightly less than 1.005, so ordinary rounding sees a value just below the tie and rounds down. This calculator works with your typed digits as exact whole numbers, so it correctly returns 1.01.
Why is rounding important?
Rounding keeps numbers readable, matches the precision your measurements can justify, and fits real limits such as currency units or manufacturing tolerances. Reporting more digits than you can support overstates how accurate a result really is.
Can rounding cause errors?
Yes. Rounding at every step lets small errors build up, and rounding percentages separately can make a table add to 99 or 101 per cent. Keep full precision through a calculation and round only the final answer.
How many decimal places should I round to?
Match the context: two decimal places for money, the precision of your instrument for measurements, and the significant figures given in the question for schoolwork. Never report more digits than your data can justify.
How do you round GST amounts?
Australian GST is 10 per cent, so dividing a GST-inclusive price by 11 gives the GST portion. A 99 dollar item contains exactly 9 dollars of GST. Round to the nearest cent at the final step rather than at each line.
What is the 5 cent rounding rule in Australia?
Because 1 cent and 2 cent coins are no longer in circulation, cash totals are rounded to the nearest 5 cents. Totals ending in 1, 2, 6 or 7 cents round down, while 3, 4, 8 or 9 cents round up. Card payments stay exact to the cent.
How do you round to the nearest quarter or eighth?
Use the nearest multiple option with 0.25 for a quarter or 0.125 for an eighth. For example, 7.3 rounded to the nearest quarter is 7.25, which is useful for imperial measurements and timber sizes.
Is this Rounding Calculator free?
Yes. It is free with no sign-up, works on any device, and runs in your browser so your entries stay private.