Rounding Rules and Significant Figures
Rounding replaces a number with an approximate value that has a shorter, simpler, or more explicit representation. It is crucial in physics, accounting, and statistics to avoid false precision.
The Standard 5-Up Rule
The universal rule taught in grade school is: look at the digit to the right of your target rounding place. If it is 5 or greater, round up. If it is 4 or less, stay the same. Rounding 3.14159 to two decimal places yields 3.14.
Banker's Rounding (Round Half to Even)
In accounting and computer science, always rounding 0.5 "up" introduces a positive bias into large datasets. IEEE 754 (used by most programming languages) uses "Banker's Rounding," where exactly 0.5 rounds to the nearest even number. 2.5 rounds to 2, and 3.5 rounds to 4. This mathematically eliminates statistical bias.