How it’s calculated
Rounding keeps a chosen number of digits (or a whole number of some unit) and discards the rest. The rules differ only when the discarded part is exactly half:
- Half up: the common school rule. A 5 rounds away from zero (2.345 → 2.35).
- Half to even: a 5 followed only by zeros rounds to the even neighbor (2.345 → 2.34, 2.355 → 2.36). NIST SP 811 uses this rule, and it avoids an upward bias when adding many rounded values.
- Up / down / toward zero: always round in one direction, regardless of the digit.
Example: 2.345 to 2 decimal places. 2.345 ÷ 0.01 = 234.5, exactly a half. Half up gives 235 × 0.01 = 2.35; half to even gives 234 × 0.01 = 2.34. To the nearest 0.05: 2.345 ÷ 0.05 = 46.9, which rounds to 47, so 47 × 0.05 = 2.35.
Numbers are handled as typed in decimal, so 2.345 is treated as exactly 2.345 rather than its nearest binary value.
Frequently asked questions
What is banker’s rounding?
Rounding halves to the nearest even digit. 0.5 → 0, 1.5 → 2, 2.5 → 2. Over many values, ups and downs balance out.
How do I round to the nearest 5 cents?
Choose "Nearest multiple of…" and enter 0.05. $2.42 → $2.40 and $2.43 → $2.45 with half up.
How do I round to the nearest thousand?
Use −3 decimal places, or a multiple of 1000. 12,499 → 12,000; 12,500 → 13,000 with half up.
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Sources
- NIST Guide to the SI, Appendix B (B.7 Rules for rounding numbers) — U.S. National Institute of Standards and Technology
- Prealgebra 2e, §5.1 Decimals (rounding decimals) — OpenStax
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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