Significant figures are the digits in a number that carry meaning about its precision. They indicate how exactly a measurement or calculation is known, and they help convey the uncertainty inherent in measuring devices and methods. Key ideas

• Definition
  • In any measured value, not all digits are equally meaningful. Significant figures are the digits that contribute to the precision of the value, starting from the first nonzero digit on the left.
• Rules for counting
  • All nonzero digits (1–9) are significant.
  • Zeros between nonzero digits are significant.
  • Leading zeros (to the left of the first nonzero digit) are not significant; they are placeholders.
  • Trailing zeros are significant if a decimal point is present; if there is no decimal point, trailing zeros may be ambiguous and may or may not be significant depending on context or notation.
• Rounding and operations
  • Addition and subtraction: the result should be rounded to the least precise decimal place among the operands (i.e., the fewest digits after the decimal point).
  • Multiplication and division: the result should have the same number of significant figures as the factor with the fewest significant figures.
• Practical interpretation
  • The number of significant figures reflects the measurement’s precision, not its magnitude. For example, 0.004520 has four significant figures (4520 when ignoring leading zeros and the decimal point).
  • When reporting results, it’s common to match the precision to the measurement that’s been made or the instrument’s capability.

Common examples

• 453.0 has four significant figures.
• 0.00452 has three significant figures (zeros are placeholders; 4, 5, and 2 are significant).
• 1200 (without a decimal) can have two to four significant figures depending on context; often needs clarification (e.g., 1.20×10^3 has three significant figures, 1200 with a bar or decimal point may indicate four).

If you want, provide a few numbers or a calculation, and the number of significant figures you’d like to report, and the rounding rules you’re following (e.g., school, scientific notation), and I can guide you step by step.