Round any number to a chosen number of significant figures.
Significant figures count all reliably known digits. We convert to scientific notation, round the mantissa to N digits, then convert back.
Significant figures are the digits in a measured (not counted or defined) number that carry real meaning — they communicate the precision of the measuring instrument or process that produced the number, not just its raw magnitude. The core counting rules: all nonzero digits are always significant; zeros between nonzero digits are always significant (105 has 3 sig figs); leading zeros before the first nonzero digit are never significant, since they're just placeholders showing decimal position (0.0025 has 2 sig figs, not 5); and trailing zeros are significant only when there's a decimal point present (2500 has an ambiguous 2-4 sig figs depending on convention, but 2500. or 2.500 × 10³ unambiguously has 4).
That trailing-zero ambiguity is exactly why scientific notation and significant figures are so often taught together — writing 2,500 in scientific notation as 2.5 × 10³ makes it unambiguous that there are 2 significant figures, while 2.500 × 10³ makes it equally clear there are 4, a distinction that's genuinely difficult to convey in standard notation. When calculating with measured numbers, the results also need to respect the least precise measurement involved — in multiplication and division, the result should be rounded to match the fewest significant figures among the inputs; in addition and subtraction, the result should be rounded to match the least number of decimal places among the inputs. This isn't a pedantic formality: a calculated answer can't honestly claim more precision than its least-precise input actually supports, and reporting extra digits beyond what the measurements justify overstates the real accuracy of the result.
All nonzero digits are always significant. Zeros between nonzero digits are always significant (105 has 3 sig figs). Leading zeros before the first nonzero digit are never significant — they're just placeholders (0.0025 has 2 sig figs). Trailing zeros are significant only when a decimal point is present.
Written as plain 2,500, it's unclear whether the trailing zeros are meaningful measured digits or just placeholders, so it could represent 2, 3, or 4 significant figures depending on convention. Scientific notation removes the ambiguity: 2.5 × 10³ unambiguously shows 2 significant figures, while 2.500 × 10³ unambiguously shows 4.
The result should be rounded to match the fewest significant figures among all the numbers used in the calculation. A calculation can't produce a result more precise than its least-precise input, since that would overstate the actual accuracy the original measurements support.
Yes — for addition and subtraction, the result is rounded to match the least number of decimal places (not significant figures) among the inputs, while multiplication and division rounds to match the fewest significant figures. These are genuinely different rules, and mixing them up is a common mistake.