Click to set the rounding method or define your own precision level.
Rounding is the mathematical process of replacing a number with an approximate value that has a simpler, shorter, or more practical representation, while remaining as close to the original value as possible.
Rounding is universally utilized in commerce (e.g. rounding prices to the nearest cent), scientific measurement (matching sensor precision limits), and computing (preventing infinite recurring decimal expansions like 1/3 = 0.3333...).
The standard method taught in school. If the discarded fractional part is ≥ 0.5, round away from zero (up in magnitude).
If the discarded value is exactly 0.5, round to the nearest even digit. This eliminates the positive upward bias inherent in summing thousands of rounded values in financial ledgers.
Always rounds upwards towards positive infinity (+∞), regardless of how small the remainder is.
Always rounds downwards towards negative infinity (-∞).
| Place Value Name | Power of 10 | Numerical Multiplier | Decimal Place |
|---|---|---|---|
| Billions | 10⁹ | 1,000,000,000 | 9 digits left of dot |
| Millions | 10⁶ | 1,000,000 | 6 digits left of dot |
| Thousands | 10³ | 1,000 | 3 digits left of dot |
| Hundreds | 10² | 100 | 2 digits left of dot |
| Tens | 10¹ | 10 | 1 digit left of dot |
| Ones (Units) | 10⁰ | 1 | Decimal Point |
| Tenths | 10⁻¹ | 0.1 | 1st decimal place |
| Hundredths | 10⁻² | 0.01 | 2nd decimal place |
| Thousandths | 10⁻³ | 0.001 | 3rd decimal place |
| Ten Thousandths | 10⁻⁴ | 0.0001 | 4th decimal place |
| Millionths | 10⁻⁶ | 0.000001 | 6th decimal place |
In standard computer binary floating point (IEEE-754), 1.005 cannot be represented exactly in binary and is stored as 1.004999999999999893... causing standard float rounders to round down. Our calculator uses exact decimal string arithmetic to ensure 1.005 correctly rounds to 1.01.
For positive numbers, truncate and floor are identical (5.9 ➔ 5). However, for negative numbers, truncate rounds towards zero (-5.9 ➔ -5), whereas floor rounds down towards -∞ (-5.9 ➔ -6).
Significant figures are the digits in a number that carry meaningful precision, beginning with the first non-zero digit. For example, 0.007894 has 4 significant figures, and rounding it to 2 sig figs yields 0.0079.