Significant Figures Calculator

Four rules cover almost every case: (1) all non-zero digits are significant; (2) zeros between non-zero digits (captive zeros) are significant - 105 has 3; (3) leading zeros are never significant - 0.045 has 2; (4) trailing zeros are significant only after a decimal point - 1.200 has 4, but 1200 is ambiguous (2 to 4). Writing a decimal point after a whole number (1200.) or using scientific notation (1.200e3) removes the ambiguity.

Three. The two leading zeros (after the 0.0) are placeholders and never significant. The 4 and 5 are non-zero digits, and the trailing zero after the decimal point is significant by rule 4. Trailing zeros after a decimal communicate instrument precision - that is why chemists write them.

Find the first three significant digits, look at the fourth to decide rounding, then replace everything after with zeros (or adjust the exponent in scientific notation). 123,456 -> the first three sig digits are 1, 2, 3 and the next is 4, so round down to 123,000. 0.005678 -> first three are 5, 6, 7 and the next is 8, so round up to 0.00568.

Multiplication follows the fewest-sig-figs rule: 2.5 has 2 sig figs and 3.42 has 3, so the result gets 2. The calculator computes 8.55 then rounds to 2 sig figs: 8.6. Reporting 8.55 would claim more precision than the 2.5 measurement supports.

Addition and subtraction are absolute-precision operations: line up the decimal points and the result keeps as many DECIMAL PLACES as the operand with the fewest. 1.2 + 2.34 = 3.5 (one decimal place, from 1.2), not 3.54. 100.1 - 2.45 = 97.6, not 97.65. Note this rule is about decimal places, not sig figs.

No - exact numbers (counted quantities like 3 trials, defined conversions like 100 cm = 1 m, and constants in formulas) have infinite significant figures and never limit a calculation. Only measured quantities carry uncertainty. A sig fig calculator is for the measured values; ignore the exact ones when deciding precision.