Significant figures

• significant figures (or significant digits) are digits that are either:
  • nonzeros
  • zeroes located between nonzero digits
  • trailing zeros in a decimal
• (remark) zero to the left of the first nonzero digit is not significant
• arithmetic rules for significant figures: (examples from (Denniston, 2022))
  • addition and subtraction: the result should be rounded to the least number of decimal places among the operands.
    • \begin{array}{r@{\enspace}l} & \phantom{0}37.68{\color{red}xxx} \\ & 108.428{\color{red}xx} \\ + & \phantom{00}6.71864 \\ \hline & 152.82{\color{red}664} & \text{(should be 152.83)} \end{array}
  • multiplication and division: the result should be rounded to the least number of significant figures among the operands.
    • $\frac{4.237\times 1.21\times 10^{-3}\times 0.00273}{11.125}=1.26\times 10^{-6}$

References

• Denniston (2022). General, Organic, and Biochemistry. McGraw-Hill Education.