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Example 1.5: Multiplication and Division with Significant Figures

Rule: When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least precise value in terms of multiplication and division).
(a) Multiply 0.6238 cm by 6.6 cm.
(b) Divide 421.23 g by 486 mL.

Solution

\(\mathrm{product}_{\mathrm{a}}\) \(= 0.6238\ \mathrm{cm} \cdot 6.6\ \mathrm{cm}\)

\(\ \ \ =4.12\ \mathrm{cm}^{2}\)


result is 4.1cm2(round to two significant figures): four significant figures × two significant figures⟶two significant figures answer

\(\mathrm{quotient}_{\mathrm{b}}\) \(= \dfrac{421.23\ \mathrm{g}}{486.\ \mathrm{mL}}\)

\(\ \ \ =0.867\ \frac{\mathrm{g}}{\mathrm{mL}}\)


result is 0.867 g/mL(round to three significant figures):five significant figures/three significant figures⟶three significant figures answer