Rounding number...
Enter a number and choose a place value or significant-figure target.
What Is a Rounding Calculator?
A rounding calculator replaces a number with a nearby value at a selected precision. This tool rounds by decimal place, whole-number place value, power of ten, or significant figures while showing the retained digit and the deciding digit. It uses exact decimal text rather than binary floating-point arithmetic, so familiar edge cases such as 1.005 to the nearest hundredth produce 1.01.
Rounding makes measurements and calculations easier to report, but a rounded answer is usually an approximation. Keep unrounded values during intermediate work whenever possible and round the final result to avoid accumulating error.
How the Deciding Digit Controls Rounding
Rounding 4.36 to the nearest tenth places the input above the midpoint 4.35, so the result is 4.4.
4.36 rounds to 4.4
For 0.004567 to two significant figures, 4 and 5 are retained, 6 decides, and the result is 0.0046.
How to Round Numbers by Place Value
Find the digit in the requested place, then inspect the digit immediately to its right. If that deciding digit is 0 through 4, keep the retained digit. If it is 5 through 9, increase the retained magnitude by one and replace less-significant whole-number places with zeros or remove less-significant decimal places.
For 8,765 rounded to the nearest hundred, the hundreds digit is 7 and the tens digit is 6. Because 6 is at least 5, the hundreds digit becomes 8 and the result is 8,800. Carry can continue across several nines, as when 999.5 rounds to 1,000.
How to Round to the Nearest Tenth or Hundredth
To round to the nearest tenth, retain the first digit after the decimal point and inspect the hundredths digit. To round to the nearest hundredth, retain the second decimal digit and inspect the thousandths digit. For 12.345 to the nearest hundredth, the deciding digit is 5, so the result is 12.35.
Decimal zeros can communicate precision. A result of 1.20 rounded to the nearest hundredth should retain both decimal places, while 1.2 communicates only the nearest tenth.
How to Round to Significant Figures
Significant figures begin at the first non-zero digit. Leading zeros only locate the decimal point, so the first two significant digits in 0.004567 are 4 and 5. The next digit is 6, which raises 5 to 6 and gives 0.0046.
When a rounded whole number ends in zeros, scientific notation states the precision clearly. The standard result 12,300 rounded to three significant figures can be written as 1.23 x 10^4, while 1,000 to two significant figures is 1.0 x 10^3.
Rounding Rules for 0 Through 9
| Target | Digit kept | Digit checked | Example |
|---|---|---|---|
| Nearest hundred | Hundreds | Tens | 1,249 -> 1,200 |
| Nearest ten | Tens | Ones | 1,249 -> 1,250 |
| Whole number | Ones | Tenths | 12.6 -> 13 |
| Nearest tenth | Tenths | Hundredths | 12.34 -> 12.3 |
| Nearest hundredth | Hundredths | Thousandths | 12.345 -> 12.35 |
| 3 significant figures | Third significant digit | Next significant digit | 12,345 -> 12,300 |
This calculator uses round half away from zero. A positive halfway value such as 2.5 becomes 3, and -2.5 becomes -3 because its magnitude increases away from zero. Some software uses half-even rounding instead, so results at exact ties can differ when another system is configured with that convention.
Rounding Negative Numbers
Apply the digit rule to the magnitude and then restore the negative sign. For -1.005 rounded to the nearest hundredth, the deciding digit is 5, so the magnitude becomes 1.01 and the result is -1.01. Saying the magnitude increases is clearer than saying the negative number rounds up.
Values whose deciding digit is below 5 move toward zero at the selected precision. The number line in the result makes the numeric direction visible and labels the selected endpoint.
Decimal Places vs Significant Figures
Decimal places count positions to the right of the decimal point. Significant figures count meaningful digits beginning with the first non-zero digit, regardless of decimal position. Therefore 0.004567 rounded to two decimal places is 0.00, while the same number rounded to two significant figures is 0.0046.
Use decimal places for fixed monetary or reporting formats and significant figures for measured precision in science and engineering. Follow the requirements of the assignment, standard, or reporting system rather than assuming the two methods are interchangeable.
Rounding Calculator FAQ
How do I round a number to the nearest tenth?
Keep the tenths digit and inspect the hundredths digit. Increase the tenths digit when the hundredths digit is 5 through 9; otherwise leave it unchanged.
How do I round to the nearest hundredth?
Keep two digits after the decimal point and inspect the thousandths digit. For example, 2.675 becomes 2.68 under the half-away-from-zero convention.
What digit do I look at when rounding?
Look at the digit immediately to the right of the place you want to retain. That digit decides whether the retained magnitude stays or increases.
Does 5 always round up?
In this calculator, an exact 5 tie rounds away from zero. Other systems may use half-even or another rule, so confirm the required convention.
How do I round a negative number?
Round the magnitude using the same deciding-digit rule and restore the sign. A negative tie such as -2.5 becomes -3 with half-away-from-zero rounding.
What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point. Significant figures begin at the first non-zero digit and describe precision across large and small magnitudes.
How do I round 0.004567 to two significant figures?
The first two significant digits are 4 and 5, and the deciding digit is 6. Increase the second digit to obtain 0.0046.
Why does 9.99 round to 10?
Rounding can carry through consecutive nines. At two significant figures, the final 9 increases the preceding 9 and creates a new tens digit.
Should I round during each calculation step?
Keep extra precision during intermediate calculations whenever possible. Repeated rounding can accumulate error, so round the final result to the required precision.
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