Rounding and Significant Figures
Rounding makes numbers easier to read and communicates how precise they are. Doing it well means choosing the right kind of rounding and the right rule.
Decimal places
Rounding to n decimal places keeps n digits after the point. Look at the next digit: 5 or more rounds up, less than 5 leaves the kept digit unchanged.
Round 3.14159 to 2 decimal places
- Kept digits: 3.14
- Next digit: 1 (less than 5)
3.14
Significant figures
Significant figures count from the first non-zero digit, regardless of where the decimal point is.
| Number | Significant figures | Why |
|---|---|---|
| 4,560 | 3 (or 4) | trailing zeros in a whole number are ambiguous |
| 0.00456 | 3 | leading zeros are not significant |
| 4.560 | 4 | a trailing zero after the point is significant |
| 1.002 | 4 | zeros between non-zero digits count |
Scientific notation removes ambiguity: 4.56 × 10³ has three significant figures, 4.560 × 10³ has four.
Rounding rules
| Rule | 2.5 → | −2.5 → | Used for |
|---|---|---|---|
| Half away from zero | 3 | −3 | school arithmetic, most receipts |
| Half to even (banker’s) | 2 | −2 | statistics, some accounting and IEEE 754 |
| Ceiling (always up) | 3 | −2 | how many boxes/buses you need |
| Floor (always down) | 2 | −3 | whole items you can afford |
| Truncate (toward zero) | 2 | −2 | dropping decimals in programming |
Half-to-even avoids a slight upward bias when many values ending in exactly 5 are rounded and summed.
Why computers sometimes “round wrong”
Computers store most decimals in binary, where values like 0.1 and 1.005 cannot be represented exactly. 1.005 is actually stored as 1.00499999999999989…, so naive code rounds it to 1.00 instead of 1.01, and 0.1 + 0.2 comes out as 0.30000000000000004. CalcoraBase rounds on the decimal digits and trims floating-point noise to 12 significant digits, so results show 0.3 and 1.01 as expected.
Good practice
- Round only at the end of a calculation, never in intermediate steps.
- Match the precision of your inputs: 12.3 cm × 4.56 cm is best reported as 56.1 cm², not 56.088 cm².
- State the rule you used when it matters (money, grades, legal thresholds).
Try the rounding calculator to compare all five rules on your own numbers.