In physics and chemistry, answers are not just about getting the right number — they’re about showing the correct level of precision. That’s where significant figures become extremely important. Many students lose marks even when their calculation is correct, simply because the final answer is not written with proper significant figures.
This guide explains how significant figures are used in physics and chemistry calculations, with clear rules, examples, and practical tips.
Why Are Significant Figures Important in Physics and Chemistry?
Measurements in science are never perfectly exact. Every measuring instrument has a limit. Significant figures tell us how precise a measurement really is.
In exams and lab work, significant figures help to:
- Show the accuracy of measurements
- Avoid giving false precision
- Ensure results match the least precise data used
- Maintain consistency in scientific reporting
Significant Figures in Physics Calculations
Physics often involves measurements, formulas, and constants. The key rule is:
👉 The final answer must match the least precise value used in the calculation.
Example 1: Speed Calculation
Speed = Distance ÷ Time
Distance = 24.6 m
Time = 3.2 s
Calculation:
24.6 ÷ 3.2 = 7.6875
Least significant figures = 2 (from 3.2)
Final Answer: 7.7 m/s
Example 2: Force Calculation
Force = mass × acceleration
Mass = 2.50 kg
Acceleration = 9.8 m/s²
Calculation:
2.50 × 9.8 = 24.5
Least significant figures = 2
Final Answer: 25 N
Significant Figures in Chemistry Calculations
Chemistry frequently uses moles, concentrations, masses, and volumes. The same rules apply, but precision becomes even more important in lab results.
Example 3: Density Calculation
Density = mass ÷ volume
Mass = 5.60 g
Volume = 2.3 cm³
Calculation:
5.60 ÷ 2.3 = 2.4348
Least significant figures = 2
Final Answer: 2.4 g/cm³
Example 4: Solution Concentration
Concentration = moles ÷ volume
Moles = 0.125 mol
Volume = 0.50 L
Calculation:
0.125 ÷ 0.50 = 0.25
Least significant figures = 2
Final Answer: 0.25 mol/L
Addition and Subtraction in Scientific Data
In both physics and chemistry:
👉 Addition and subtraction depend on decimal places, not sig figs
Example
12.45 g + 3.2 g = 15.65 g
Least decimal places = 1
Final Answer: 15.6 g
Common Mistakes in Physics & Chemistry Exams
- Rounding during intermediate steps
- Ignoring the least precise measurement
- Mixing decimal-place rules with sig-fig rules
- Writing too many digits in the final answer
- Forgetting units after rounding
Step-by-Step Method for Solving Scientific Problems
- Write down all given values with units
- Perform the full calculation without rounding
- Identify the limiting value (fewest sig figs or decimals)
- Round only the final answer
- Recheck units and precision
Quick Exam Tip
If your final answer looks more precise than your measurements, it’s probably wrong. Precision should never increase during calculations.
FAQs
How to calculate significant figures in physics?
In physics, significant figures are calculated by following these steps:
- Identify the number of significant figures in each measured value
- Perform the calculation without rounding
- Find the value with the fewest significant figures
- Round the final answer to match that number of significant figures
This ensures the result reflects the precision of the measurements used.
How are significant figures used in chemistry?
In chemistry, significant figures are used to show the precision of measurements in calculations involving mass, volume, moles, concentration, and density.
The final answer must have the same number of significant figures as the least precise measurement used in the calculation.
This prevents reporting results that appear more accurate than the experimental data.
Are significant figures in chemistry and physics the same?
Yes, the rules for significant figures are exactly the same in both chemistry and physics.
Only the type of measurements and formulas change, not the rounding rules.
Both subjects follow:
- Sig figs for multiplication and division
- Decimal places for addition and subtraction
How do you write 57.3997 correctly to 4 significant figures?
Step 1: First four significant digits → 5, 7, 3, 9
Step 2: Look at the next digit (9)
Since 9 is greater than or equal to 5, round up.
Answer: 57.40
(The zero shows that the value has four significant figures.)