Significant Figures — Rules and rounding
Units & Measurements
10
JEE Qs
8%
Hard
60
min
Apply significant figure rules only to the final answer in multi-step calculations to avoid premature rounding errors, unless intermediate rounding is explicitly specified.
✅ Key Points for JEE
- 1All non-zero digits are significant. Zeros between non-zero digits are significant.
- 2Leading zeros (zeros before non-zero digits) are never significant. Trailing zeros are significant ONLY if the number contains a decimal point.
- 3For addition and subtraction, the final result must be rounded to the same number of decimal places as the measurement with the fewest decimal places.
- 4For multiplication and division, the final result must be rounded to the same number of significant figures as the measurement with the fewest significant figures.
- 5Rounding Rule: If the digit to be dropped is > 5, increase the preceding digit by 1. If < 5, keep the preceding digit the same. If = 5, increase the preceding digit by 1 if it is odd, and keep it the same if it is even.
⚠️ Common Mistakes
- ✕Incorrectly identifying significant figures, especially with leading and trailing zeros (e.g., 0.0025 vs. 2.500).
- ✕Confusing the rules for addition/subtraction (decimal places) with those for multiplication/division (significant figures).
- ✕Making errors in rounding when the digit to be dropped is exactly 5, by not applying the odd/even rule correctly.
📝 Practice Questions
See allQ43.The maximum percentage error in the measurment of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g radius of wire = (0.50 ± 0.01)cm length of wire = (10.00 ± 0.05)cm] (1) 8 (2) 5 (3) 4 (4) 7 for another diatomic molecules, but for rigid molecules and γ2 =
Q43.The energy of a system is given as E(t) = α3e−βt , where t is the time and β = 0.3 s−1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s, maximum percentage error in the energy is : (1) 6% (2) 8.4% (3) 11.6% (4) 4%
Q39.Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below. (1) Statement I is true but Statement II is false (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
Q40.Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge, (1) [F] = [C2M−1 L−2 T2] (2) [F] = [C2M−2 L2 T2] (3) [F] = [CM−2 L−2 T−2] (4) [F] = [CM−1 L−2 T2]
Q28.The position of a particle moving on x-axis is given by x(t) = A sin t + B cos2 t + Ct2 + D , where t is time. The dimension of ABC is D (1) L2T −2 (2) L2 (3) L (4) L3 T−2
Q45.For an experimental expression y = 32.3×112527.4 , where all the digits are significant. Then to report the value of y we should write (1) y = 1326.19 (2) y = 1330 (3) y = 1326.186 (4) y = 1326.2
NCERT Chapters
- Class 11 Physics Ch 2: Units and Measurements