Units and Measurement Notes for NEET and JEE Main 2027 with PDF

Units and Measurement is Chapter 1 of NCERT Class 11 Physics and Unit 1 of both the NEET UG and JEE Main syllabi. These notes cover SI base and derived units, significant figures and rounding off, errors in measurement, dimensions, dimensional formulae and dimensional analysis, with high-yield facts, common mistakes and a free notes PDF.

Units and Measurement Notes for NEET and JEE Main

Section-wise key points from NCERT Chapter 1, rules and formula tables, high-yield facts and common mistakes for 2027 revision.

Units and Measurement at a Glance

The topic list follows the NEET UG 2026 syllabus released by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus published by the National Testing Agency (NTA). Both stay the reference until the 2027 syllabi are out. Full lists: NEET syllabus and JEE Main syllabus.

What are base units, derived units and SI?

A unit is an internationally accepted reference standard used to measure a physical quantity. The units of the base quantities are base (fundamental) units; units of all other quantities, made from combinations of base units, are derived units.

• A complete set of base and derived units is a system of units.
• Older systems: CGS (centimetre, gram, second), FPS or British (foot, pound, second) and MKS (metre, kilogram, second).
• The internationally accepted system today is the Système International d’Unités (SI), with seven base units.
• Two more units are defined: radian (rad) for plane angle, dθ = ds/r, and steradian (sr) for solid angle, dΩ = dA/r². Both are dimensionless.
• SI base units are now defined by fixing the numerical values of constants such as the speed of light c, the Planck constant h, the elementary charge e, the Boltzmann constant k and the Avogadro constant. NCERT notes that these values need not be memorised.

When the mole is used, the elementary entities (atoms, molecules, ions, electrons or other particles) must be specified. One mole contains exactly 6.02214076 × 10²³ entities.

Significant figures: how do you count them?

Significant figures are the reliable digits of a measurement plus the first uncertain digit. They show the precision of a measurement, which depends on the least count of the instrument.

• All non-zero digits are significant.
• All zeros between two non-zero digits are significant, wherever the decimal point is.
• For a number less than 1, zeros to the right of the decimal point but left of the first non-zero digit are not significant (0.002308 has four significant figures).
• Trailing zeros in a number without a decimal point are not significant (123 m = 12300 cm = 123000 mm has three).
• Trailing zeros in a number with a decimal point are significant (3.500 and 0.06900 have four each).
• The zero conventionally written to the left of the decimal in a number less than 1 (as in 0.1250) is never significant.
• Changing units does not change the number of significant figures: 2.308 cm = 0.02308 m = 23.08 mm, all four significant figures.
• Scientific notation (a × 10ᵇ) removes the ambiguity: 4.700 m = 4.700 × 10³ mm, still four significant figures.
• Exact numbers in formulas (the 2 in s = 2πr, or n in T = t/n) have an infinite number of significant figures.

Order of Magnitude

• Round a in a × 10ᵇ to 1 if a ≤ 5 and to 10 if 5 < a ≤ 10; the resulting power b is the order of magnitude.
• Diameter of the earth (1.28 × 10⁷ m): order of magnitude 7. Diameter of a hydrogen atom (1.06 × 10⁻¹⁰ m): order −10. So the earth is 17 orders of magnitude larger.

Rules for Arithmetic with Significant Figures

Rounding Off the Uncertain Digits

• If the digit dropped is more than 5, raise the preceding digit by 1; if less than 5, leave it unchanged: 2.746 → 2.75, 1.743 → 1.74.
• If the digit dropped is exactly 5: drop it when the preceding digit is even (2.745 → 2.74) and raise the preceding digit when it is odd (2.735 → 2.74).
• In multi-step calculations keep one extra digit in intermediate steps and round off only at the end. Example: 1/9.58 = 0.104, but 1/0.104 = 9.62; keeping 0.1044 returns 9.58.
• The relative error of a value depends on the number itself: ±0.01 g in 1.02 g is about ±1%, but in 9.89 g it is about ±0.1%.

Least Count and Errors in Measurement

These topics are in both the NEET UG and JEE Main syllabi but are not in the rationalised NCERT chapter; the points below follow the older NCERT edition.

• Least count is the smallest value that an instrument can measure; every reading is uncertain to about one least count.
• Accuracy is how close a measured value is to the true value. Precision is the resolution, or the limit to which the quantity is measured. A measurement can be precise without being accurate.

Combination of Errors

NCERT’s worked example: l = 16.2 ± 0.1 cm (about 0.6%) and b = 10.1 ± 0.1 cm (about 1%), so the area lb = 164 ± 3 cm².

Dimensions and Dimensional Formulae

The dimensions of a physical quantity are the powers (exponents) to which the base quantities are raised to represent it. Square brackets [ ] mean ‘the dimensions of’.

• The seven dimensions are length [L], mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd] and amount of substance [mol].
• In mechanics every quantity can be written in terms of [M], [L] and [T].
• Magnitudes do not enter dimensions: change in velocity, initial velocity, average velocity and speed all have dimensions [L T⁻¹].
• A dimensional formula shows which base quantities, and with what powers, make up a quantity; equating a quantity to it gives a dimensional equation, for example [F] = [M L T⁻²].

Dimensional Analysis and Its Applications

Dimensional analysis has two main uses in the chapter: checking whether an equation is dimensionally consistent and deducing a relation among physical quantities.

Checking the Consistency of Equations

• Principle of homogeneity: only quantities with the same dimensions can be added, subtracted or equated, so every term of a correct equation has the same dimensions.
• Example: in x = x₀ + v₀t + ½at², every term has dimension [L], so the equation is dimensionally correct.
• A dimensionally wrong equation must be wrong, but a dimensionally correct equation need not be correct; it is uncertain to the extent of dimensionless factors.
• Arguments of trigonometric, logarithmic and exponential functions must be dimensionless.
• Example 1.4: for kinetic energy, K = m²v³, K = ma and K = ½mv² + ma are ruled out; dimensions cannot choose between ½mv² and (3/16)mv².

Deducing Relations Among Quantities

• Assume a product form of dependence on up to three independent quantities and equate powers of M, L and T.
• Simple pendulum: T = k lˣ gʸ mᶻ gives x = ½, y = −½, z = 0, so T = k√(l/g). The constant k (= 2π) cannot be found by this method.

Limitations

• Dimensionless constants cannot be obtained.
• It cannot tell apart quantities that have the same dimensions (for example work and torque).
• It tests only dimensional validity, not the exact relationship.

Most-asked Facts for NEET and JEE Main: Units and Measurement

Revise these one-line facts from the chapter just before the exam.

• SI has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela.
• Radian and steradian are dimensionless units of plane angle and solid angle.
• Significant figures do not change when units change.
• Trailing zeros count only when the number has a decimal point.
• Multiply or divide: fewest significant figures. Add or subtract: fewest decimal places.
• 2.745 rounds to 2.74 (preceding digit even); 2.735 rounds to 2.74 (preceding digit odd).
• Absolute errors add for sums and differences; relative errors add for products and quotients.
• For Z = Aᵏ, the relative error is k times the relative error of A.
• Force [M L T⁻²], work and energy [M L² T⁻²], power [M L² T⁻³], pressure [M L⁻¹ T⁻²].
• Momentum and impulse share the dimensions [M L T⁻¹].
• A dimensionally correct equation can still be wrong; a dimensionally wrong one is always wrong.
• Dimensional analysis gives T = k√(l/g) for a pendulum but cannot give k = 2π.
• Order of magnitude of the earth’s diameter is 7; that of a hydrogen atom is −10.

Common Mistakes to Avoid

Watch for these mix-ups when you answer questions on this chapter.

• Counting the leading zeros of 0.002308 as significant. It has four significant figures, not seven.
• Rounding the sum 663.821 g to 664 g. Addition follows decimal places, so the answer is 663.8 g.
• Rounding every x.xx5 upwards. With an even preceding digit the 5 is simply dropped.
• Adding percentage errors for a sum. For Z = A + B the absolute errors add, not the percentage errors.
• Forgetting the power: for Z = A³ the relative error is 3ΔA/A.
• Treating radian or refractive index as having dimensions. Both are dimensionless.
• Assuming dimensional analysis proves an equation correct. It can only rule equations out.
• Confusing accuracy with precision. Precision is the resolution of the measurement; accuracy is closeness to the true value.

Units and Measurement Notes PDF and Related Pages

Download the AglaSem notes for Units and Measurement (key notes and important questions with answers) free: View PDF

• All chapters: Physics notes for NEET and JEE Main
• Full topic lists: NEET syllabus and JEE Main syllabus
• Practice: NEET question papers and JEE Main question papers
• Source text: NCERT Chapter 1 (NCERT, Class 11 Physics Part I)

Physics Notes for NEET and JEE Main: All Chapters

• Units and Measurement
• Motion in a Straight Line
• Motion in a Plane
• Laws of Motion
• Work, Energy and Power
• Systems of Particles and Rotational Motion
• Gravitation
• Mechanical Properties of Solids
• Mechanical Properties of Fluids
• Thermodynamics
• Kinetic Theory of Gases
• Oscillations
• Waves
• Thermal Properties of Matter
• Electric Charges and Fields
• Electrostatic Potential and Capacitance
• Current Electricity
• Moving Charges and Magnetism
• Magnetism and Matter
• Electromagnetic Induction
• Electromagnetic Waves
• Ray Optics and Optical Instruments
• Wave Optics
• Dual Nature of Radiation and Matter
• Atoms
• Nuclei
• Semiconductor Electronics

All chapters with key points and notes PDFs are on the Physics notes for NEET and JEE Main page.

Units and Measurement Notes for NEET and JEE Main FAQs