The trap that costs marks on significant figures is deceptively simple: aspirants apply the wrong rounding rule to the wrong arithmetic operation. Multiplication and division require rounding to the fewest significant figures among the inputs. Addition and subtraction require rounding to the fewest decimal places. Swapping these two rules is a high-frequency mistake on NEET (NCERT Class 11 Physics Chapter 1, pages 4–5).
What are significant figures? Every measured quantity carries uncertainty. Significant figures are the digits in a measurement that are known reliably plus the first uncertain digit (NCERT Class 11 Physics Chapter 1, page 3). They encode the precision of the instrument that produced the number.
Counting rules (NCERT conventions):
The two rounding rules:
Watch out: When a subtraction problem like 9.99 m − 0.0099 m appears, the fewest decimal places is 2 (from 9.99). The answer is 9.98 m — not 9.9801 m (keeping all digits) and not 1.0 × 10¹ m (wrongly applying the sig-fig rule). This is the exact trap NEET has tested.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
How many significant figures are in the measurement 0.00470 kg?
The number 8.0 × 10⁴ has how many significant figures?
Which of the following numbers has exactly 4 significant figures?
A rectangular plate has length 4.234 m and breadth 1.05 m. The area of the plate, expressed with the correct number of significant figures, is:
The result of 28.4 m + 2.175 m, expressed with the correct number of significant figures, is:
A student measures two lengths as 12.50 m and 2.1 m and subtracts them: 12.50 − 2.1 = 10.40. The correctly rounded result is:
Two rods are measured as 5.2 cm and 3.34 cm. Their difference is calculated as 5.2 − 3.34 = 1.86 cm. A student reports the answer as 1.9 cm. Another student reports it as 2 cm. Which student is correct and why?
A student computes the area of a square sheet with side 2.1 cm as 2.1 × 2.1 = 4.41 cm². She then subtracts the area of a small hole, 0.065 cm², from the sheet area. What is the correct final answer?
Given
Two measured lengths: L₁ = 9.99 m (2 decimal places, 3 sig figs) and L₂ = 0.0099 m (4 decimal places, 2 sig figs).
Required
Find L₁ − L₂ expressed with the correct number of significant figures.
Concept
When measured quantities are subtracted, the result must be rounded to the fewest decimal places among the inputs — not the fewest significant figures. This is the addition/subtraction rounding convention (NCERT Class 11 Physics Chapter 1, page 5).
Formula
For Z = A ± B: round Z to the fewest decimal places among A and B.
Substitution
Raw subtraction: 9.99 − 0.0099 = 9.9801 m. Decimal places: L₁ has 2 decimal places; L₂ has 4 decimal places. The fewest is 2.
Calculation
9.9801 rounded to 2 decimal places → 9.98 m. No exact constants are involved in this problem — both numbers are measured quantities with inherent uncertainty.
Final answer
**9.98 m** (3 significant figures, 2 decimal places). Note: if we had wrongly applied the multiplication/division rule (fewest sig figs = 2, from 0.0099), we would get 1.0 × 10¹ m — a drastically different and incorrect answer.
Common trap
The most common error is applying the "fewest significant figures" rule to this subtraction. L₂ = 0.0099 has only 2 significant figures, which tempts students to round the answer to 2 sig figs (giving 10 m or 1.0 × 10¹ m). But subtraction demands the decimal-place rule, not the sig-fig rule.
Similar NEET-style question
Two masses are measured: m₁ = 25.0 g and m₂ = 0.034 g. Express (m₁ − m₂) with the correct significant figures. *Answer: 25.0 − 0.034 = 24.966 → fewest decimal places is 1 (from 25.0) → 25.0 g.* ---
All the reliably-known digits in a measured quantity, plus the first uncertain (estimated) digit, are called significant figures. Significant figures indicate the precision of measurement.
-- NCERT Class 11 Physics, Ch. 1, p. 3Rules: (i) all non-zero digits are significant; (ii) zeros between non-zero digits are significant; (iii) leading zeros (before the first non-zero digit) in a decimal number are NOT significant; (iv) trailing zeros in a number without a decimal point are NOT significant; (v) trailing zeros after a decimal point ARE significant. Exact numbers (counted, definitions) have unlimited significant figures.
-- NCERT Class 11 Physics, Ch. 1, p. 4Multiplication/division: result has the same number of significant figures as the input with the fewest significant figures. Addition/subtraction: result has the same number of decimal places as the input with the fewest decimal places.
-- NCERT Class 11 Physics, Ch. 1, p. 5A cube has side measured as 7.203 m (4 sig figs). Surface area 6 × 7.203² = 311.299254 m² rounded to 311.3 m² (4 sig figs). Volume 7.203³ = 373.714754 m³ rounded to 373.7 m³ (4 sig figs).
-- NCERT Class 11 Physics, Ch. 1, p. 6The maximum relative error in a power expression is the sum of the absolute exponents weighted by the relative errors of the bases. Negative exponents (divisions) still take the |.| value because we want the worst-case error.
| Symbol | Quantity | SI Unit |
|---|---|---|
| Z | Result | (combined) |
| p, q, r | Exponents (signed) | (dimensionless) |
| A, B, C | Measured quantities | (measured) |
When two measured quantities are multiplied or divided, the maximum RELATIVE errors add. The absolute error in the result is then Delta_Z = Z * (relative-error sum).
| Symbol | Quantity | SI Unit |
|---|---|---|
| Z | Result of product/quotient | (combined unit) |
| A | First measured quantity | (measured) |
| B | Second measured quantity | (measured) |
| Delta_A/A | Relative error in A | (dimensionless) |
| Delta_B/B | Relative error in B | (dimensionless) |
When two quantities are added or subtracted, the maximum absolute errors of the inputs simply add to give the maximum absolute error of the output. The relative error is NOT what adds in this case.
| Symbol | Quantity | SI Unit |
|---|---|---|
| Z | Result of sum/difference | (same as A,B) |
| A | First measured quantity | (measured) |
| B | Second measured quantity | (measured) |
| Delta_Z | Maximum absolute error in Z | (same as A,B) |
| Delta_A | Maximum absolute error in A | (same as A) |
| Delta_B | Maximum absolute error in B | (same as B) |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Category: Similar Terms
Student gets the time exponent wrong by 1 (e.g. T⁻¹ vs T⁻²) when manipulating dimensional formulas.
Question asks for dimensions of a derived combination (e.g. E/G, F = αt² + βt) where time exponent matters.
Write each base quantity's dimensional formula explicitly, then combine. Common errors: dividing forces forgets sub of T exponents; energy/length includes implicit time. Always check final units against expected SI.
Category: Similar Terms
Student sums relative errors of all measured quantities without weighting by the exponent. For ρ = m/(πr²L), the relative error contribution of r is 2 × Δr/r, NOT Δr/r — the exponent of r in the formula carries through as a multiplicative factor.
Question gives a derived quantity formula with mixed-power dependencies; asks for the max relative error. Distractors omit the power factor.
Always write the full general rule: for Z = A^p B^q C^r, ΔZ/Z = |p|·ΔA/A + |q|·ΔB/B + |r|·ΔC/C. Identify the powers (1, 2, 3, ½) before adding.
Category: Similar Terms
Student conflates random errors (statistical, unpredictable, reduced by averaging) with instrumental errors (consistent bias from the apparatus) or with systematic errors (consistent bias from the method). Each has a distinct definition and different mitigation.
Question describes an error source and asks for its taxonomic category. Distractors include cognate categories.
Memorise the 5-category taxonomy: PERSONAL (observer-side), INSTRUMENTAL (apparatus calibration), LEAST-COUNT (instrument resolution floor), RANDOM (statistical, reduced by repeated trials), SYSTEMATIC (method-level bias, NOT reduced by averaging).
Category: Similar Terms
Student swaps which is the input vs the output: least count = pitch / N (where N is the number of circular-scale divisions). Distractors offer the ratio inverted or the wrong unit.
Question gives one of (pitch, N, least count) and asks for another; distractors offer the inverted ratio or off-by-factor-of-10.
Anchor on the definition: least count is the SMALLEST measurement the instrument can resolve. It is always SMALLER than the pitch. So pitch = LC × N (and not LC = pitch × N).
Category: Similar Terms
Student applies the 'fewest significant figures' rule (which governs multiplication and division) to a sum or difference. Subtraction of two measured numbers must instead reflect the FEWEST decimal places.
Question involves addition/subtraction of measured numbers with very different magnitudes or decimal-place counts (e.g. 9.99 - 0.0099). Distractors offer answers rounded by sig-fig rule rather than decimal-place rule.
Memorise: multiplication/division → fewest SIGNIFICANT FIGURES; addition/subtraction → fewest DECIMAL PLACES. Always identify which arithmetic operation is being performed before applying any rule.
Category: Similar Terms
Student treats radian/steradian as having dimensions because they have unit names.
Question asks about dimensions of plane angle, solid angle, or comparison.
Plane angle (radian) and solid angle (steradian) are DIMENSIONLESS — they're ratios (arc/radius for radian; surface-area/r² for steradian). They have unit NAMES for clarity but no dimensions.
Category: Similar Terms
Confusing whether N or N+1 is the smaller count when (N+1) divisions of vernier match N divisions of main scale.
Question gives '(N+1) divisions of vernier coincide with N divisions of main' or similar phrasing.
Always interpret carefully: N+1 vernier divisions span the SAME LENGTH as N main divisions. So 1 VSD = (N/(N+1)) MSD; vernier constant = 1 MSD - 1 VSD = 1 MSD / (N+1). Result smaller than 1 MSD.
Root cause: formula misuse
Use Delta_Z = Delta_A + Delta_B for sums/differences (absolute errors add). Use Delta_Z/Z = Delta_A/A + Delta_B/B for products/quotients (relative errors add). They are NOT interchangeable — the rule is dictated by whether the operation is additive or multiplicative.
Distractor option uses the wrong rule (e.g. quotes a small relative error for a sum where absolute errors should add).
Root cause: concept gap
For multiplication/division, the result has the fewest significant figures of any input. For addition/subtraction, the result has the fewest decimal places of any input. Decimal places ≠ significant figures.
Distractor truncates a sum to too few significant figures by applying the multiplication rule.
The quantities which have the same dimensions as those of solid angle are :
The dimensions [MLT–2A–2] belong to the
Plane angle and solid angle have
miscounts power of T
Off-by-one on time exponent (e.g. -1 vs -2)
forgets power of two on radius
Default to summing all relative errors with weight 1
linear sum no powers
Adding all relative errors with weight 1
treats radian as dimensional
Confuses 'has unit' with 'has dimensions'
instrumental misclassified as random
Both feel 'unavoidable'; need to recognise instrumental ≠ random
swaps pitch and LC
Confusing which side of the formula is asked
no rounding
Calculator answer kept verbatim
applies mult rule to subtraction
Default to 'fewest sig figs' without distinguishing subtraction's decimal-places rule
swap N and N+1
Confusing which side has the larger count
Test yourself on this topic with real past-paper questions:
Practice this topic →Get a structured 30-day Mechanics plan and a complete formula booklet — delivered to your inbox instantly.