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Rounding Calculator

Round to decimal places, significant figures or the nearest multiple — with seven rounding methods and exact arithmetic.

Quick Answer: How Do You Round a Number?

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.

Round a Number

Any number, positive or negative. Commas and spaces are ignored.

Copied!
Result
Rounded to 2 decimal places
3.14
Original: 3.14159265
Every methodResult
Why this calculator gets 1.005 right. Most rounding tools store numbers in binary, where 1.005 is really 1.00499999…, so they return 1.00. This one works with the digits you typed as exact whole numbers, so 1.005 rounds to 1.01 — the answer you would get by hand.

What Is Rounding?

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.

The Rounding Formulas

decimal places: round(x × 10d) ÷ 10d
nearest multiple: round(x ÷ m) × m
significant figures: round at the (sf − 1 − ⌊log₁₀|x|⌋) decimal place

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.

How to Use the Calculator

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 Seven Rounding Methods

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.

MethodRule2.5 → 0 dp−2.5 → 0 dpTypical use
Half up (standard)Ties go away from zero3−3School maths, everyday rounding
Half downTies go toward zero2−2Conservative estimates
Half to even (banker's)Ties go to the nearest even digit2−2Finance, statistics, IEEE 754
Away from zeroAlways increases the magnitude3−3Safety margins, material ordering
Toward zero (truncate)Simply drops the extra digits2−2Computing, integer division
Ceiling (toward +∞)Always goes up the number line3−2Pricing, capacity planning
Floor (toward −∞)Always goes down the number line2−3Age, 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.

Rounding Cheat Sheet

Quick reference

Nearest whole: 4.7 → 5   Nearest tenth: 4.74 → 4.7
Nearest hundredth: 4.746 → 4.75   Nearest thousandth: 4.7463 → 4.746
3 significant figures: 4567 → 4570   2 sig figs: 0.004567 → 0.0046
Nearest 10: 178 → 180   Nearest 100: 1234 → 1200
Nearest 1,000: 45,678 → 46,000   Nearest cent: $4.567 → $4.57
Nearest quarter: 7.3 → 7.25   Nearest half: 7.3 → 7.5

Worked Examples

1. Round 3.14159 to 2 decimal places

Keep two decimals: 3.14 | next digit is 1
1 is below 5, so the 4 stays
3.14

2. Round 4876 to 3 significant figures

Count three digits from the first non-zero: 4, 8, 7
The next digit is 6, so the 7 rounds up to 8
4880

3. Round 178 to the nearest 5

178 ÷ 5 = 35.6
35.6 rounds to 36 · 36 × 5 = 180
180

4. Round 1.005 to 2 decimal places

The next digit is exactly 5, so it is a tie
Half up sends the tie away from zero
1.01 — note that many calculators wrongly give 1.00 here

5. Round −4.55 to 1 decimal place

Ignore the sign and round 4.55 → 4.6 (half up)
Put the sign back
−4.6 · with ceiling instead you would get −4.5

6. Round 0.000456 to 2 significant figures

Leading zeros are not significant — start counting at 4
The two significant digits are 4 and 5; the next digit is 6, so the 5 rounds up
0.00046

7. Money: round $12.3449 to the nearest cent

Cents means two decimal places
The next digit is 4, so it rounds down
$12.34

8. Banker's rounding across a set

Half up: 0.5, 1.5, 2.5, 3.5 → 1, 2, 3, 4 (total 10)
Half to even: 0.5, 1.5, 2.5, 3.5 → 0, 2, 2, 4 (total 8)
The true total is 8 — half to even removes the upward drift

Decimal Places vs Significant Figures

FeatureDecimal placesSignificant figures
Counted fromThe decimal pointThe first non-zero digit
0.004567 to 30.0050.00457
4567 to 34567.0004570
Leading zerosCounted as placesNever significant
Best forMoney and fixed unitsMeasurements and science

Common Rounding Targets

Round toSettingExample
Nearest whole number0 decimal places4.7 → 5
Nearest tenth1 decimal place4.74 → 4.7
Nearest hundredth2 decimal places4.746 → 4.75
Nearest thousandth3 decimal places4.7463 → 4.746
Nearest cent2 decimal places$4.567 → $4.57
Nearest dollar0 decimal places$4.67 → $5
Nearest 10Multiple of 10178 → 180
Nearest 100Multiple of 1001234 → 1200
Nearest 1,000Multiple of 100045,678 → 46,000
Nearest millionMultiple of 10000007,499,000 → 7,000,000
Nearest quarterMultiple of 0.257.3 → 7.25
Nearest eighthMultiple of 0.1257.3 → 7.25

Rounding Money

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.

Rounding in Finance, GST and Tax

Money is where rounding rules matter most, because small differences repeat across thousands of transactions.

SituationRuleExample
Card or bank paymentNearest cent (2 dp)$12.3449 → $12.34
Australian cash paymentNearest 5 cents$12.34 → $12.35
GST on a priceNearest cent, per the ATO$99 ÷ 11 = $9.00 GST
Adding GSTMultiply by 1.1, then round$45.45 × 1.1 = $49.995 → $50.00
Tax return figuresWhole dollars$1,234.67 → $1,235
Interest calculationsFull precision, round at the endRound only the final balance
Share pricesOften 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.

Rounding Negative Numbers

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.

Real-Life Uses of Rounding

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.

Common Mistakes

Watch out for these:
  • Confusing decimal places with significant figures. 0.004567 is 0.005 to 3 decimal places but 0.00457 to 3 significant figures.
  • Counting leading zeros as significant. In 0.00456 the zeros only hold the place; counting starts at the 4.
  • Rounding in stages. Taking 2.346 to 2.35 and then to 2.4 gives the wrong answer — 2.346 to 1 decimal place is 2.3.
  • Rounding intermediate steps. Keep full precision through a calculation and round only the final figure.
  • Using the wrong method in finance. Always rounding ties upward creates a small but real upward bias across many transactions.
  • Assuming the calculator is exact. Ordinary floating-point maths misreads values like 1.005; this page avoids that by using exact digit arithmetic.
  • Forgetting trailing zeros carry meaning. Writing 3.1 when 3.10 was asked for drops a significant figure.

Practice Questions

Beginner (with answers)

  1. Round 6.48 to 1 decimal place.
  2. Round 12.5 to the nearest whole number (half up).
  3. Round 3,472 to the nearest 100.
  4. Round 0.0837 to 2 decimal places.
  5. Round $8.435 to the nearest cent.
Show answers

1) 6.5   2) 13   3) 3,500   4) 0.08   5) $8.44

Advanced (with answers)

  1. Round 0.004982 to 3 significant figures.
  2. Round −7.5 to the nearest whole number using floor.
  3. Round 6.5 and 7.5 to whole numbers using banker's rounding.
  4. Round 13.7 to the nearest 0.25.
  5. Round 2,499,500 to the nearest million.
Show answers

1) 0.00498   2) −8   3) 6 and 8 (both go to the even digit)   4) 13.75   5) 2,000,000

Did you know? Banker's rounding is the default in the IEEE 754 standard that nearly every computer uses for decimal arithmetic. The reason is bias: if you always send ties upward, a long column of figures creeps steadily higher. Sending half the ties down keeps the total honest.
Pro tip. Round once, at the end. Every intermediate rounding adds its own small error, and those errors compound through a long calculation.
Pro tip. Use the "every method" table on this page to sanity-check a disputed figure. If two methods disagree, you have found exactly where a spreadsheet and a colleague's answer parted ways.

🔑 Key Takeaways

  • Look at the next digit: 5 or more rounds up, 4 or less rounds down
  • Decimal places count from the point; significant figures count from the first non-zero digit
  • Banker's rounding sends ties to the nearest even digit and avoids upward bias
  • Ceiling and floor differ from away-from-zero and toward-zero only on negative numbers
  • Round once at the end, never at every step

Frequently Asked Questions

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.

References

Last updated: July 2026
Reviewed by Mohsin Iqbal using standard rounding conventions and trusted educational references. Calculations use exact integer arithmetic on the digits you enter rather than binary floating-point, so tie cases such as 1.005 and 2.675 round the way they do by hand. This page is for educational purposes and is not financial advice.