Significant Figures in Multiplication and Division
Physics · Units And Measurements · NEET
When you multiply or divide measured values, the answer must keep the same number of significant figures as the value that has the fewest significant figures. Example: 55.3 (3 sig figs) times 25 (2 sig figs) gives an answer with only 2 sig figs. Memory hook: "Multiply and divide - the smallest count decides."
In multiplication and division, count significant figures in each measured value. The value with the fewest sig figs (here 25 with 2) sets how many sig figs the final answer keeps, so 1382.5 rounds to 14 x 10 to the power 2.
Your doubts, answered
Do I count decimal places or significant figures when I multiply?
For multiplication and division you count significant figures, NOT decimal places. This is the opposite of addition and subtraction. In multiply/divide, find which measured value has the fewest significant figures, and give your final answer with that many significant figures. Example: 2.5 (2 sig figs) x 3.42 (3 sig figs) = 8.55, but you round to 2 sig figs = 8.6.
Why is my answer only 2 significant figures when the calculator shows 6 digits?
The calculator does exact arithmetic, but your measurements are not exact. If one value was measured to only 2 significant figures (like 25 m), your final answer cannot be more precise than that. So even though 55.3 x 25 = 1382.5 on the calculator, the true reliable answer is 14 x 10 to the power 2 (2 sig figs). Extra digits are false precision.
How is this different from the addition and subtraction rule?
Two different rules. Add/subtract: match the fewest DECIMAL PLACES. Multiply/divide: match the fewest SIGNIFICANT FIGURES. NCERT warns you not to mix them up. If a question adds first then multiplies, apply each rule at its own step.
Do exact numbers or pure counts limit significant figures?
No. Exact numbers (like the 2 in 2 pi r, or counting 5 readings) have infinite significant figures, so they never limit the answer. Only measured values with uncertainty control the sig-fig count of the final result.
⚠️ The NEET trap ✗ Writing 55.3 x 25 = 1382.5 m squared and picking that as the answer because it looks exact. ✓ 25 has only 2 significant figures, so the area must be rounded to 2 sig figs: 1382.5 becomes 14 x 10 to the power 2 m squared. 🧠 NTA loves giving you an extra-precise-looking decimal option as bait.
Real NEET questions
NEET 2022
The area of a rectangular field (in m squared) of length 55.3 m and breadth 25 m, after rounding off the value for correct significant digits, is:
A · 138 x 10 to the power 1
B · 1382
C · 1382.5
D · 14 x 10 to the power 2 ✓
Solution: Step 1: Multiply the raw values. Area = 55.3 x 25 = 1382.5 m squared. Step 2: Count significant figures. 55.3 has 3 sig figs; 25 has 2 sig figs. The smaller count is 2. Step 3: Round 1382.5 to 2 significant figures. The first two significant digits are 1 and 3; the next digit is 8, so round up to 14 followed by the zeros. Result = 14 x 10 to the power 2 m squared. Answer: D.
NEET 2026
Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X x 10 to the power 3 kg per m cubed, where the value of X is:
A · 7.654
B · 7.6
C · 7.65
D · 7.7 ✓
Solution: Step 1: Convert side to metres. 9.0 cm = 0.090 m. Volume = (0.090) cubed = 7.29 x 10 to the power minus 4 m cubed. Step 2: Density = mass / volume = 5.580 / (7.29 x 10 to the power minus 4) = 7654 kg per m cubed = 7.654 x 10 to the power 3. Step 3: Count significant figures. Mass 5.580 has 4 sig figs; side 9.0 has only 2 sig figs. The smallest count is 2. Step 4: Round 7.654 to 2 sig figs = 7.7. So X = 7.7. Answer: D.
Solved Units And Measurements NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the significant figures rule for multiplication and division?
The final answer keeps the same number of significant figures as the measured value that has the fewest significant figures. Count sig figs in every measured value, take the smallest count, and round your answer to that many sig figs.
Is the multiplication rule based on decimal places?
No. Multiplication and division use significant figures. Only addition and subtraction use decimal places. Mixing these up is the most common NEET mistake.
How do I count significant figures in a number like 0.090?
Leading zeros are not significant. In 0.090 the two zeros before 9 do not count, but the 9 and the trailing zero after it do, giving 2 significant figures.
When do I round off, before or after the calculation?
Do the full calculation first with all digits, then round the final answer once to the correct number of significant figures. Rounding at intermediate steps can add error.
