Why do calculators disagree about rounding 1.005 to two decimal places?

Because 1.005 cannot be stored exactly in binary floating point. What actually sits in memory is 1.00499999999999989341858963598497211933135986328125, which is below the halfway point, so most languages round down to 1.00, which is correct for the number they were given. This tool works on the digits you typed as an exact decimal, so it treats 1.005 as exactly 1005/1000 and rounds to 1.01. Neither is a bug; they are answers to different questions, and the tool tells you when the two diverge.

What are the tie-breaking rules and which should I use?

Choose the rule required by your calculation or assignment. Half up sends an exact midpoint toward positive infinity: 2.5 becomes 3 and −2.5 becomes −2. Half away from zero sends these to 3 and −3. Half even chooses an even number of grid steps at a tie: 2.5 becomes 2 and 3.5 becomes 4. This is also called banker’s rounding. The page shows all ten rules, and any one can drive the result; it does not choose a standard or policy for you.

Why do the rules differ on negative numbers?

Because "up" is ambiguous once you cross zero. Half up takes −2.5 to −2, since −2 is the larger number. Half away from zero takes it to −3, since 3 is the larger magnitude. Both are called "round half up" in different documentation, which is exactly why this tool names the rule rather than assuming one.

What is the difference between decimal places and significant figures?

Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.001234 to three decimal places is 0.001, which throws away nearly all the information. To three significant figures it is 0.00123, which preserves it. Measurements are almost always better expressed in significant figures.

Can I round to the nearest 5, 25 or 0.1?

Choose Multiple and enter the step as a decimal. Use 5 for the nearest five, 0.05 for five-cent increments, 0.5 for halves or 0.125 for eighths. For example, 0.38 at a step of 0.125 gives 0.375 under Half up. Results use decimal notation; this input does not accept a slash fraction such as 1/8. A negative step has the same grid as its positive magnitude, and zero has no rounding grid.

Does it handle very large or very small numbers?

It rounds accepted decimal and scientific-notation inputs without converting the answer to a binary double. For example, 1.234e6 is 1,234,000. Decimal-place counts range from −100,000 to 100,000, and significant-figure counts from 1 to 100,000. A request needing excessive working is refused with an explanation; a very long plain result uses scientific notation. Abbreviated supporting values are marked ≈, so read their labels before copying them.

How do I round to the nearest tenth, hundredth, thousandth or whole number?

Choose Decimals and enter 1 for a tenth, 2 for a hundredth, 3 for a thousandth or 0 for a whole number. Under Half up, 12.3456 becomes 12.3, 12.35, 12.346 or 12 respectively. The hundredth page opens the two-place job. A hundred and a hundredth are different targets: use −2 decimal places or a Multiple step of 100 for the nearest hundred.

How do I round to tens, hundreds, thousands or millions?

Use Decimals with −1 for tens, −2 for hundreds, −3 for thousands, −4 for ten thousands, −5 for hundred thousands, −6 for millions or −7 for ten millions. Multiple accepts the same steps, including 10, 100, 1,000 and 1,000,000. Under Half up, 126 rounds to 130 at tens and 100 at hundreds; 12,600 rounds to 13,000 at thousands. Select the target once and round the original value, rather than rounding the already rounded answer again.

How are round up, round down and truncation different?

Ceiling always moves toward positive infinity: 2.1 becomes 3 and −2.9 becomes −2 at zero decimal places. Floor always moves toward negative infinity: 2.9 becomes 2 and −2.1 becomes −3. Truncate drops unwanted digits toward zero, so −2.9 becomes −2. Away from zero always increases the magnitude. These are selectable rules, not the Half up or Half down midpoint rules; always state which one you need for negative values.

Can I round money, percentages, grades or measurements?

Enter the numeric coefficient without a currency symbol, percent sign or unit. For 12.345 dollars, two decimal places give 12.35 under Half up; a Multiple step of 0.05 uses five-cent increments. For 12.346%, enter 12.346 and keep the percent unit with the rounded result: two places give 12.35%. Measurements in degrees, metres, feet, centimetres or grams keep the same entered unit. A grade or amount follows the rule you select; no syllabus, tax, payroll, cash-rounding or measurement policy is inferred.

What does three-digit rounding or rounding to the greatest place mean?

If you mean three significant digits, choose Sig figs and enter 3; 12.345 becomes 12.3. If you mean a number rounded at a place such as hundreds, choose that decimal-place target instead. One significant figure rounds directly at the greatest nonzero place: 25,446 becomes 30,000 under Half up. These controls round one supplied value. They do not evaluate arithmetic expressions or simulate a sequence of three- or four-digit arithmetic operations.

Can I use front-end rounding or rounding all the way?

For a single-value front-end truncation, choose Sig figs, enter 1 and select Truncate: 4,382 becomes 4,000, while nearest Half up gives 4,000 for this value too but differs on 4,882, giving 5,000. Front-end estimation of several operands and round-all-the-way worksheets can require additional steps or adjustment rules. This page does not run those algorithms automatically. Direct rounding and sequential rounding differ: 1.449 goes directly to 1.4 at one decimal place, while rounding first to two places gives 1.45, then 1.5 at one place under Half up.

Can this round fractions, clock times or calculated expressions?

The input is one decimal or scientific-notation value, not a slash fraction, ratio, HH:MM clock time or expression. A decimal step such as 0.125 works exactly, but converting a repeating fraction to a finite decimal first can change a boundary decision. For a known numeric duration in minutes, a step of 15 rounds those minutes; it does not calculate a timecard or apply a work-time rule. Significant Figures Calculator provides separate two-number arithmetic with its stated precision rules, including the Addition page. Neither tool here simulates rounding after each operation in an arbitrary expression.

Will opening a rounding preset replace my saved values and rule?

A preset supplies the settings named for that page during the visit. The hundredth and thousand pages open their worked examples under Half up. Other saved settings remain available. Only a value or setting you explicitly edit is remembered; opening a preset does not replace the saved draft, and an unfinished entry is retained so you can correct it.

Rounding Calculator

Round to decimal places, significant figures or the nearest multiple, with the tie-breaking rule named on every result. It rounds the number you typed rather than the binary approximation of it, which is why it can answer 1.01 for 1.005 where most programming languages answer 1.00. Choose Decimals for a place such as the nearest tenth or cent, Multiple for a step such as 5 or 0.125, or Sig figs for a chosen number of significant digits. The rule selector includes ceiling, floor and truncation as well as nearest rounding; these directed rules can change a value even when it is not halfway.

2 decimal places · half up2.68A 64-bit float would answer differently here, see below

Value

Round to

Places

Rule

Round to a fixed number of digits after the point. A negative count rounds to the left of the point instead: −3 rounds to the nearest thousand.

Half up. Nearest neighbour; an exact midpoint goes up the number line, toward +∞. So 2.5 → 3 and −2.5 → −2. This is what most people were taught at school, and it is not symmetric about zero.

Heads up: this is the classic rounding bug. You typed 2.675, which sits exactly on the midpoint as a decimal, so half up gives 2.68. But a 64-bit binary float cannot store 2.675 exactly. JavaScript, Python, Java and C actually hold 2.674999999999999822364316…, which is a hair below the number you typed, so they answer 2.67 instead. Neither is a mistake, they are rounding a slightly different number. This page rounds the one you typed.

2.675 sits exactly halfway between 2.67 and 2.68. That is a tie, and the tie rule is what decides it: Half up sends ties up the number line, so the answer is 2.68.

Resulthalf up
2.68
Scientifichow many digits are actually claimed
2.68 × 10⁰
For codee-notation, ready to paste
2.68e+0
Differencethe answer minus what you typed
+0.005
Grid pointsthe two values your number falls between
2.67 → 2.68
How this was readthe exact decimal these answers are built from
2.675
The exact stored valuewhat a 64-bit float really holds, not the number you typed
2.67499999999999982236431605997495353221893310546875

The same number under all ten rules. Where they disagree none of them is wrong; they are different rules, and this is exactly where two spreadsheets quietly stop matching.

Rule	Result	Where you meet it
Half up · your rule	2.68	JavaScript Math.round(), school rounding
Half down	2.67	rare on its own; the mirror of half up
Half to even (banker's)	2.68	IEEE 754 default, Python round(), C# Math.Round(), NumPy
Half to odd	2.67	some signal-processing code; uncommon elsewhere
Half away from zero	2.68	Excel ROUND(), PHP round(), Java BigDecimal HALF_UP, most SQL engines
Half toward zero	2.67	Java BigDecimal HALF_DOWN
Ceiling	2.68	Math.ceil(), Excel CEILING()
Floor	2.67	Math.floor(), Excel INT()
Truncate (toward zero)	2.67	Math.trunc(), Excel TRUNC(), integer casts in C, Go and Rust
Away from zero	2.68	Excel ROUNDUP()

This rounds the number you typed, not the binary copy of it. Ask almost any language for 1.005 to two decimal places and it answers 1.00, because a 64-bit float cannot hold 1.005. What it holds is 1.00499999999999989, a hair below the midpoint, so the tie never happens. The arithmetic here is exact decimal, so 1.005 gives 1.01, and wherever that choice changes the answer this page says so and shows the value actually held in memory.

Rounding by place value

Examples use Half up for positive numbers. Select another tie rule when your assignment or application requires one.

Round to	Control	Example
Nearest tenth	Decimals: 1	12.346 → 12.3
Nearest hundredth	Decimals: 2	12.346 → 12.35
Nearest thousandth	Decimals: 3	12.3456 → 12.346
Nearest ten	Multiple: 10	126 → 130
Nearest hundred	Multiple: 100	126 → 100
Nearest thousand	Multiple: 1000	12,600 → 13,000

Common questions

Why do calculators disagree about rounding 1.005 to two decimal places?: Because 1.005 cannot be stored exactly in binary floating point. What actually sits in memory is 1.00499999999999989341858963598497211933135986328125, which is below the halfway point, so most languages round down to 1.00, which is correct for the number they were given. This tool works on the digits you typed as an exact decimal, so it treats 1.005 as exactly 1005/1000 and rounds to 1.01. Neither is a bug; they are answers to different questions, and the tool tells you when the two diverge.
What are the tie-breaking rules and which should I use?: Choose the rule required by your calculation or assignment. Half up sends an exact midpoint toward positive infinity: 2.5 becomes 3 and −2.5 becomes −2. Half away from zero sends these to 3 and −3. Half even chooses an even number of grid steps at a tie: 2.5 becomes 2 and 3.5 becomes 4. This is also called banker’s rounding. The page shows all ten rules, and any one can drive the result; it does not choose a standard or policy for you.
Why do the rules differ on negative numbers?: Because "up" is ambiguous once you cross zero. Half up takes −2.5 to −2, since −2 is the larger number. Half away from zero takes it to −3, since 3 is the larger magnitude. Both are called "round half up" in different documentation, which is exactly why this tool names the rule rather than assuming one.
What is the difference between decimal places and significant figures?: Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.001234 to three decimal places is 0.001, which throws away nearly all the information. To three significant figures it is 0.00123, which preserves it. Measurements are almost always better expressed in significant figures.
Can I round to the nearest 5, 25 or 0.1?: Choose Multiple and enter the step as a decimal. Use 5 for the nearest five, 0.05 for five-cent increments, 0.5 for halves or 0.125 for eighths. For example, 0.38 at a step of 0.125 gives 0.375 under Half up. Results use decimal notation; this input does not accept a slash fraction such as 1/8. A negative step has the same grid as its positive magnitude, and zero has no rounding grid.
Does it handle very large or very small numbers?: It rounds accepted decimal and scientific-notation inputs without converting the answer to a binary double. For example, 1.234e6 is 1,234,000. Decimal-place counts range from −100,000 to 100,000, and significant-figure counts from 1 to 100,000. A request needing excessive working is refused with an explanation; a very long plain result uses scientific notation. Abbreviated supporting values are marked ≈, so read their labels before copying them.
How do I round to the nearest tenth, hundredth, thousandth or whole number?: Choose Decimals and enter 1 for a tenth, 2 for a hundredth, 3 for a thousandth or 0 for a whole number. Under Half up, 12.3456 becomes 12.3, 12.35, 12.346 or 12 respectively. The hundredth page opens the two-place job. A hundred and a hundredth are different targets: use −2 decimal places or a Multiple step of 100 for the nearest hundred.
How do I round to tens, hundreds, thousands or millions?: Use Decimals with −1 for tens, −2 for hundreds, −3 for thousands, −4 for ten thousands, −5 for hundred thousands, −6 for millions or −7 for ten millions. Multiple accepts the same steps, including 10, 100, 1,000 and 1,000,000. Under Half up, 126 rounds to 130 at tens and 100 at hundreds; 12,600 rounds to 13,000 at thousands. Select the target once and round the original value, rather than rounding the already rounded answer again.
How are round up, round down and truncation different?: Ceiling always moves toward positive infinity: 2.1 becomes 3 and −2.9 becomes −2 at zero decimal places. Floor always moves toward negative infinity: 2.9 becomes 2 and −2.1 becomes −3. Truncate drops unwanted digits toward zero, so −2.9 becomes −2. Away from zero always increases the magnitude. These are selectable rules, not the Half up or Half down midpoint rules; always state which one you need for negative values.
Can I round money, percentages, grades or measurements?: Enter the numeric coefficient without a currency symbol, percent sign or unit. For 12.345 dollars, two decimal places give 12.35 under Half up; a Multiple step of 0.05 uses five-cent increments. For 12.346%, enter 12.346 and keep the percent unit with the rounded result: two places give 12.35%. Measurements in degrees, metres, feet, centimetres or grams keep the same entered unit. A grade or amount follows the rule you select; no syllabus, tax, payroll, cash-rounding or measurement policy is inferred.
What does three-digit rounding or rounding to the greatest place mean?: If you mean three significant digits, choose Sig figs and enter 3; 12.345 becomes 12.3. If you mean a number rounded at a place such as hundreds, choose that decimal-place target instead. One significant figure rounds directly at the greatest nonzero place: 25,446 becomes 30,000 under Half up. These controls round one supplied value. They do not evaluate arithmetic expressions or simulate a sequence of three- or four-digit arithmetic operations.
Can I use front-end rounding or rounding all the way?: For a single-value front-end truncation, choose Sig figs, enter 1 and select Truncate: 4,382 becomes 4,000, while nearest Half up gives 4,000 for this value too but differs on 4,882, giving 5,000. Front-end estimation of several operands and round-all-the-way worksheets can require additional steps or adjustment rules. This page does not run those algorithms automatically. Direct rounding and sequential rounding differ: 1.449 goes directly to 1.4 at one decimal place, while rounding first to two places gives 1.45, then 1.5 at one place under Half up.
Can this round fractions, clock times or calculated expressions?: The input is one decimal or scientific-notation value, not a slash fraction, ratio, HH:MM clock time or expression. A decimal step such as 0.125 works exactly, but converting a repeating fraction to a finite decimal first can change a boundary decision. For a known numeric duration in minutes, a step of 15 rounds those minutes; it does not calculate a timecard or apply a work-time rule. Significant Figures Calculator provides separate two-number arithmetic with its stated precision rules, including the Addition page. Neither tool here simulates rounding after each operation in an arbitrary expression.
Will opening a rounding preset replace my saved values and rule?: A preset supplies the settings named for that page during the visit. The hundredth and thousand pages open their worked examples under Half up. Other saved settings remain available. Only a value or setting you explicitly edit is remembered; opening a preset does not replace the saved draft, and an unfinished entry is retained so you can correct it.

Exact decimal rounding for accepted inputs, using BigInt arithmetic on the supplied digits. Requested working and output lengths have processing bounds; abbreviated supporting values are marked ≈. A separate comparison shows how rounding a binary floating-point approximation can differ.