Significant Figures Practice – Multistep Calculations
Name: ________________________
Date: _________________________
Problem 1
\n$\frac{25.6 \times 13.45}{2.3}$
Perform the calculation and round to the correct number of significant figures.
Final Answer: __________________
Problem 2
\n$(0.00456 + 12.45 + 1.2) \times 3.45$
Perform the calculation and round to the correct number of significant figures.
Final Answer: __________________
Problem 3
\n$\frac{456.2 - 123.45}{0.00567 \times 3.44}$
Perform the calculation and round to the correct number of significant figures.
Final Answer: __________________
Problem 4
\n$\frac{(6.022 \times 10^{23}) \times (0.000245)}{12.5 + 0.345}$
Perform the calculation and round to the correct number of significant figures.
Final Answer: __________________
Reminder:
- For multiplication/division, round to the least number of sig figs.
- For addition/subtraction, round to the least precise decimal place.
Significant Figures Practice – Answer Key
Notes: For multiplication/division, final result uses the least number of significant figures among factors.
For addition/subtraction, round the intermediate sum/difference to the least precise decimal place.
Problem 1
Compute: (25.6 × 13.45) over 2.3
Step 1 (×): 25.6 × 13.45 = 344.32 (keep guard digits).
Step 2 (÷): 344.32 ÷ 2.3 = 149.704...
Sig figs: factors have 3 sf, 4 sf, and 2 sf → final to 2 sf.
Final: 1.5 × 102 (i.e., 150 with 2 sf).
Problem 2
Compute: (0.00456 + 12.45 + 1.2) × 3.45
Step 1 (+): 0.00456 + 12.45 + 1.2 = 13.65456 → round to 1 decimal place (least precise) → 13.7.
Step 2 (×): 13.7 × 3.45 = 47.265.
Sig figs: 13.7 (3 sf) and 3.45 (3 sf) → final to 3 sf.
Final: 47.3
Problem 3
Compute: (456.2 − 123.45) over (0.00567 × 3.44)
Step 1 (−): 456.2 − 123.45 = 332.75 → round to 1 decimal place → 332.8.
Step 2 (×): 0.00567 × 3.44 = 0.0195048 → to 3 sf → 0.0195.
Step 3 (÷): 332.8 ÷ 0.0195 = 1.70666... × 104.
Sig figs: numerator ~4 sf, denominator 3 sf → final to 3 sf.
Final: 1.71 × 104
Problem 4
Compute: ((6.022 × 1023) × 0.000245) over (12.5 + 0.345)
Step 1 (+): 12.5 + 0.345 = 12.845 → round to 1 decimal place → 12.8.
Step 2 (×): (6.022 × 1023) × 0.000245 = 1.47539 × 1020 → to 3 sf → 1.48 × 1020.
Step 3 (÷): (1.48 × 1020) ÷ 12.8 = 1.15625 × 1019.
Sig figs: 3 sf ÷ 3 sf → final to 3 sf.
Final: 1.16 × 1019
Tip: Keep extra guard digits in intermediate steps; round only after each operation’s rule has been
applied.
