Why Significant Figures Matter in Calculations
When combining measured values through calculations, the precision of the final answer is inherently limited by the least precise measurement used. Significant figures (sig figs) provide a standardized way to express this level of precision, preventing results from implying an accuracy greater than what the original data justifies. Correctly applying these rules is fundamental for maintaining integrity and reliability in scientific and engineering computations.
Rules for Multiplication and Division
For calculations involving multiplication or division, the result should be rounded to have the same number of significant figures as the measurement with the *fewest* significant figures. For example, if you multiply 3.4 cm (two sig figs) by 1.234 cm (four sig figs), the raw answer is 4.1956 cm². However, since 3.4 cm has only two significant figures, the final result must be rounded to two significant figures, yielding 4.2 cm².
Rules for Addition and Subtraction
When adding or subtracting measured values, the result should be rounded to the same number of *decimal places* as the measurement with the *fewest* decimal places. For instance, adding 12.3 g (one decimal place) to 4.567 g (three decimal places) gives a raw sum of 16.867 g. Since 12.3 g has the fewest decimal places (one), the final answer must be rounded to one decimal place, resulting in 16.9 g.
Ensuring Accuracy in Practice
Applying these rules helps ensure that scientific results are reported with appropriate certainty. In multi-step calculations, it's generally best to carry extra digits through intermediate steps and only apply the significant figure rules at the very end to minimize rounding errors. This systematic approach ensures that conclusions drawn from calculations accurately reflect the precision limitations of the experimental data.