Physics · Ch 1 — Nature of Physical World and Measurement
Rounding Off
1.7.2
Rounding Off
A calculator's raw output almost always has more digits than the measured data justify -- the result must never be quoted with more significant figures than the least-precise input carried. Rounding off trims the extra digits using five consistent rules (Table 1.10): drop a digit smaller than 5 unchanged; round a digit greater than 5 up; a dropped '5' followed by non-zero digits always rounds up; and for a dropped '5' with nothing (or only zeros) after it, the preceding digit is left alone if it's already even, and bumped up if it's odd -- the 'round to even' convention, which avoids systematically biasing repeated rounding in one direction. …
Table 1.10Rules for Rounding Off
| Rule | Example |
|---|---|
| i) If the digit to be dropped is smaller than 5, the preceding digit is left unchanged | 7.32 -> 7.3; 8.94 -> 8.9 |
| ii) If the digit to be dropped is greater than 5, the preceding digit is increased by 1 | 17.26 -> 17.3; 11.89 -> 11.9 |
| iii) If the digit to be dropped is 5 followed by non-zero digits, the preceding digit is raised by 1 | 7.352 -> 7.4; 18.159 -> 18.2 |
| iv) If the digit to be dropped is 5, or 5 followed by zeros, the preceding digit is unchanged if it is even | 3.45 -> 3.4; 8.250 -> 8.2 |