Significant Figures Calculator

Significant figures are the digits in a recorded value that communicate its precision. They include digits known with confidence and the final estimated digit. Scientists, engineers, and students use significant figures to avoid implying more measurement certainty than an instrument provides. The written form matters: 5, 5.0, and 5.00 have the same mathematical value, but they conventionally communicate one, two, and three significant figures. Every nonzero digit is significant. Zeros between nonzero digits are also significant, so 1002 contains four significant figures. Leading zeros only locate the decimal point and are not significant; 0.0045 has two significant figures. Trailing zeros to the right of a decimal are significant, which makes 0.0520 a three-significant-figure value. Trailing zeros in a whole number without a decimal point are conventionally ambiguous. This calculator follows the common classroom rule of not counting those ambiguous trailing zeros. Scientific notation removes that ambiguity because every digit in the coefficient is significant. The value 1.20e3 clearly has three significant figures, while 1.2e3 clearly has two. Exponent digits do not affect the count. The calculator analyzes the coefficient exactly as typed, preserving trailing decimal zeros that would disappear if the input were immediately converted to an ordinary JavaScript number. Rounding to significant figures begins at the first nonzero digit. Look one digit beyond the requested precision: if that digit is five or greater, increase the retained final digit; otherwise leave it unchanged. Thus 18,439 rounded to three significant figures is 18,400, and 0.009472 rounded to two is 0.0095. The scientific-notation result makes the intended precision explicit even when an ordinary whole-number result ends in zeros. Significant-figure rules for calculations depend on the operation. Multiplication and division generally use the smallest significant-figure count among measured inputs. Addition and subtraction instead use the least precise decimal place. Keep extra digits during intermediate steps and round once at the end to reduce accumulated error. Exact counts and defined constants do not restrict precision. This calculator handles counting and direct rounding, while the meaning of the final precision should still reflect the quality and context of the original data.