Significant Figures in Lab Calculations

Given

• Volume measured: 25.0 mL (3 significant figures)

• Concentration: 1.25 M (3 significant figures)

• Masses weighed: 12.5 g (known to the tenths place) and 0.25 g (known to the hundredths place).

Find

Each result rounded to the correct number of significant figures or decimal places.

Principle

For multiplication and division, the answer carries the same number of significant figures as the least precise input. For addition and subtraction, the answer is rounded to the decimal place of the least precise input (fewest digits after the decimal point), because absolute uncertainty adds rather than scaling.

Formula

Solution

1. (a) Convert mL to L: 25.0 mL = 0.0250 L (still 3 significant figures).

2. Multiply: 0.0250 L x 1.25 mol/L = 0.03125 mol.

3. Both inputs have 3 significant figures, so round the result to 3: 0.0313 mol.

4. (b) Add: 12.5 g + 0.25 g = 12.75 g.

5. The tenths place (12.5 g) is less precise than the hundredths place (0.25 g), so round to one decimal place: 12.8 g.

Unit check

Part (a): L x mol/L = mol, so the answer is in moles as required. Part (b): g + g = g, so the total is in grams. Rounding does not change units, only the reported precision.

What this means physically

The multiplication is limited to 3 significant figures by both inputs, giving 0.0313 mol. The addition is limited by the tenths place of 12.5 g, giving 12.8 g. Reporting extra digits would falsely imply the instruments were more precise than they are — significant figures are honest advertising of measurement precision.