Chemistry · General chemistry I · Worked example
Round a density calculation correctly
An empty flask has a mass of 45.216 g. Filled with 25.0 mL of a liquid, it has a mass of 72.95 g. What is the density of the liquid, to the correct number of significant figures?
Find the mass by subtraction
72.95 g − 45.216 g = 27.734 g on a calculator. Subtraction follows the decimal-place rule, and 72.95 has two decimal places, so the mass is 27.73 g.
Divide by the volume
27.73 g ÷ 25.0 mL = 1.1092 g/mL on a calculator. In a Chemistry box this row reads ✓ for the arithmetic, with a note that the measurements support only three significant figures.
Round to the fewest significant figures
Division follows the significant-figure rule. 27.73 has four significant figures and 25.0 has three, so the density has three: 1.11 g/mL.
Why each rule applied where it did
The subtraction set the mass to four significant figures, 27.73 g, even though 45.216 g has five. The volume, with three, then limited the density. Carrying the unrounded 27.734 g into the division gives 1.1094 g/mL, which also rounds to 1.11 g/mL.
Result
The density is 1.11 g/mL.
Your turn
A rectangle measures 12.5 cm by 3.2 cm. What is its area, to the correct number of significant figures?
Show the answer and explanation
4.0 × 10¹ cm².
12.5 × 3.2 = 40.0 cm² on a calculator. 3.2 has two significant figures, so the area has two. Writing 40 cm² is ambiguous, because the trailing zero may or may not count, so scientific notation makes it clear: 4.0 × 10¹ cm².
Keep exploring
Open the rows in a Chemistry box: 1.1092 g/mL reads ✓, with a note that the measurements support three significant figures, 1.11.
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