CBSE Class 11 Physics Revision Notes Chapter 1: Units and Measurement

Units and Measurement introduces standard units, significant figures and dimensions used to express physical quantities correctly. In CBSE Class 11 Physics, these concepts support numerical calculations, unit conversions and dimensional verification.

Measurement means comparing a physical quantity with an internationally accepted reference standard called a unit. Every measurement contains a numerical value and a unit, such as 5 m, 20 kg or 10 s.

These CBSE Class 11 Physics Revision Notes Chapter 1 follow the current 2026–27 chapter. The Class 11 Physics Chapter 1 notes cover units, measurement rules, significant figures and dimensional analysis.

Key Takeaways

• Seven SI base units: SI includes seven internationally accepted base units.
• Significant figures: They include all reliable digits and the first uncertain digit.
• Dimensional formula: It expresses a physical quantity using powers of base quantities.
• Homogeneity principle: Both sides of a valid physical equation have the same dimensions.

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Access Class 11 Physics Chapter 1 Units and Measurement Notes in 30 Minutes

The chapter on Units and Measurements Class 11 builds the foundation for later numerical work in Physics. It explains how quantities are measured, recorded and checked for dimensional correctness.

Measurement, Physical Quantities and Units

Measurement compares an unknown physical quantity with a fixed standard. The result is written as a numerical value followed by a unit.

For example, in 4.5 m:

• 4.5 is the numerical value.
• m is the unit of length.

Physical Quantity

A physical quantity is a measurable property expressed through a numerical value and a unit.

Length, mass, time, velocity, force and energy are physical quantities.

Unit

A unit is an internationally accepted standard used to measure a physical quantity.

A suitable unit must be:

• Well-defined
• Easily reproducible
• Internationally accepted
• Independent of changing physical conditions

Fundamental and Derived Quantities

Physical quantities are classified as fundamental or derived.

Speed is derived from length and time:

Speed = Distance/Time

Fundamental and Derived Units

The units of base quantities are called fundamental units. Units formed by combining them are called derived units.

A complete collection of base and derived units forms a system of units.

Systems of Units

Different systems of units were used before the adoption of SI.

The SI system is now used internationally for scientific, technical, industrial and commercial work.

International System of Units in Class 11 Physics

The International System of Units is abbreviated as SI. These SI units provide standard symbols and definitions for physical measurements.

SI follows the decimal system. This makes conversions between multiples and submultiples easier.

Seven SI Base Quantities and Units

All other physical units can be expressed using these seven base units.

Plane Angle and Solid Angle

Plane angle and solid angle are dimensionless quantities used with SI.

For a plane angle:

θ = Arc length/Radius

For a solid angle:

Ω = Intercepted area/Radius²

The numerator and denominator have the same dimensions. Therefore, both ratios are dimensionless.

Rules for Writing SI Units

• Place a space between a number and its unit.
• Do not add a full stop after a unit symbol.
• Unit symbols do not have plural forms.
• Symbols named after scientists begin with capital letters.
• Unit names remain lowercase when written in full.
• Write kilogram as kg, not Kg.
• Write second as s, not sec.

Correct examples include 5 m, 12 kg, 20 s and 15 N.

Scientific Notation and Order of Magnitude

Large and small measurements are easier to express using powers of 10. Scientific notation also prevents confusion about trailing zeros.

Scientific Notation

A number in scientific notation is written as:

a × 10ᵇ

Here:

• a is greater than or equal to 1 and less than 10.
• b is a positive or negative integer.

Examples:

• 2,300,000 = 2.3 × 10⁶
• 0.00045 = 4.5 × 10⁻⁴
• 6,400 = 6.4 × 10³

The power of 10 changes when the decimal point moves. The physical quantity remains unchanged.

Order of Magnitude

The order of magnitude gives the approximate power of 10 representing a physical quantity.

The diameter of Earth is approximately:

1.28 × 10⁷ m

Its order of magnitude is 10⁷ m.

The diameter of a hydrogen atom is approximately:

1.06 × 10⁻¹⁰ m

Its order of magnitude is 10⁻¹⁰ m.

The diameter of Earth is therefore about 17 orders of magnitude larger than that of a hydrogen atom.

Significant Figures in Class 11 Physics Units and Measurement Notes

Every measurement contains some uncertainty. Significant figures show the precision with which a quantity has been measured.

They include all digits known reliably and the first uncertain digit.

For example, 1.62 s has three significant figures. The digits 1 and 6 are reliable, while 2 is uncertain.

Accuracy and Precision

Accuracy and precision describe different qualities of measurement.

Accuracy shows how close a measured value is to the accepted value. Precision shows how closely repeated measurements agree with one another.

A set of readings can be precise without being accurate. This may happen when an instrument has a systematic error.

Rules for Counting Significant Figures

The zero before the decimal in 0.25 is not significant. It only shows the position of the decimal point.

Effect of Changing Units

Changing the unit does not change the number of significant figures.

For example:

2.308 cm = 0.02308 m = 23.08 mm

Each value contains four significant figures.

Scientific notation preserves the intended trailing zeros:

4.700 m = 4.700 × 10² cm

4.700 m = 4.700 × 10³ mm

4.700 m = 4.700 × 10⁻³ km

Every expression contains four significant figures.

Arithmetic Operations with Significant Figures

A calculated result cannot be more precise than the measurements used to obtain it.

Multiplication and Division

The final answer should contain the same number of significant figures as the value with the fewest significant figures.

Example:

Mass = 5.74 g
Volume = 1.2 cm³

Density = Mass/Volume

Density = 5.74/1.2

Density = 4.7833… g cm⁻³

The volume contains two significant figures. Therefore:

Density = 4.8 g cm⁻³

Addition and Subtraction

The final answer should retain the same number of decimal places as the value with the fewest decimal places.

Example:

436.32 g + 227.2 g + 0.301 g = 663.821 g

The least precise value contains one decimal place. Therefore:

Final answer = 663.8 g

Addition and subtraction use decimal places rather than the total number of significant figures.

Rounding Off Uncertain Digits

Use the following rules while rounding numbers:

• If the dropped digit is less than 5, leave the preceding digit unchanged.
• If the dropped digit is greater than 5, increase the preceding digit by 1.
• If the dropped digit is exactly 5, check the preceding digit.
• Leave an even preceding digit unchanged.
• Increase an odd preceding digit by 1.

Examples:

• 1.743 becomes 1.74 to three significant figures.
• 2.746 becomes 2.75 to three significant figures.
• 2.745 becomes 2.74 to three significant figures.
• 2.735 becomes 2.74 to three significant figures.

Retain one extra digit during intermediate calculations. Round the answer only after completing the calculation.

Error Analysis and Uncertainty in Calculations

Error analysis helps represent uncertainty in measured and calculated quantities.

Suppose:

l = 16.2 ± 0.1 cm

b = 10.1 ± 0.1 cm

The percentage uncertainty in length is:

Percentage uncertainty in l = (0.1/16.2) × 100

Percentage uncertainty in l = 0.6%

The percentage uncertainty in breadth is:

Percentage uncertainty in b = (0.1/10.1) × 100

Percentage uncertainty in b = 1%

For multiplication, percentage uncertainties are added:

Percentage uncertainty in area = 0.6% + 1%

Percentage uncertainty in area = 1.6%

The calculated area is:

l × b = 163.62 cm²

The absolute uncertainty is approximately 2.6 cm². Therefore:

Area = 164 ± 3 cm²

Dimensions of Physical Quantities

The dimensions of physical quantities describe their nature using base quantities.

In mechanics, most quantities are expressed through:

• Mass: [M]
• Length: [L]
• Time: [T]

Meaning of Dimensions

Dimensions are the powers to which base quantities are raised when representing a physical quantity.

Volume is the product of three lengths:

Volume = Length × Breadth × Height

Therefore:

[Volume] = [L] × [L] × [L]

[Volume] = [L³]

Force is the product of mass and acceleration:

Force = Mass × Acceleration

Acceleration = Length/Time²

Therefore:

[Force] = [M][L][T⁻²]

[Force] = [MLT⁻²]

Dimensional Formula

A dimensional formula shows how a physical quantity depends on fundamental quantities.

The general dimensional formula in mechanics is:

[MᵃLᵇTᶜ]

Here, a, b and c are the powers of mass, length and time.

Examples:

• Volume = [M⁰L³T⁰]
• Velocity = [M⁰LT⁻¹]
• Acceleration = [M⁰LT⁻²]
• Force = [MLT⁻²]

Dimensional Equations

Dimensional equations equate physical quantities with their dimensional formulae.

Examples:

[Velocity] = [M⁰LT⁻¹]

[Force] = [MLT⁻²]

[Energy] = [ML²T⁻²]

These equations represent the nature of quantities. They do not show their numerical values.

Common Dimensional Formulae

Different physical quantities may have the same dimensions. Work and torque both have dimensions [ML²T⁻²].

Dimensional Analysis and Its Applications

Dimensional analysis uses dimensional formulae to examine physical equations and relationships.

The main applications of dimensional analysis include:

• Checking dimensional consistency
• Deriving relationships between physical quantities
• Converting units between different systems

Principle of Homogeneity

The principle of homogeneity states that all terms in a valid physical equation must have the same dimensions.

Consider:

v = u + at

Dimensions of v:

[v] = [LT⁻¹]

Dimensions of u:

[u] = [LT⁻¹]

Dimensions of at:

[at] = [LT⁻²][T]

[at] = [LT⁻¹]

All terms have the same dimensions. Therefore, the equation is dimensionally consistent.

Checking Dimensional Consistency

Consider:

s = ut + ½at²

Dimensions of s:

[s] = [L]

Dimensions of ut:

[ut] = [LT⁻¹][T]

[ut] = [L]

Dimensions of at²:

[at²] = [LT⁻²][T²]

[at²] = [L]

Both terms on the right have the dimensions of length. Therefore, the equation is dimensionally consistent.

A dimensionally incorrect equation is certainly wrong. However, dimensional consistency alone cannot prove that an equation is completely correct.

Deriving Relations Between Physical Quantities

Suppose the time period T of a simple pendulum depends on its length l and acceleration due to gravity g.

Assume:

T ∝ lᵃgᵇ

Therefore:

T = k lᵃgᵇ

Here, k is a dimensionless constant.

Writing the dimensions:

[T] = [L]ᵃ[LT⁻²]ᵇ

[T] = [Lᵃ⁺ᵇT⁻²ᵇ]

Comparing the powers of time:

-2b = 1

b = -1/2

Comparing the powers of length:

a + b = 0

a = 1/2

Therefore:

T = k√(l/g)

Dimensional analysis gives the form of the relation. It cannot determine the value of k.

Converting Units

A physical quantity has the same dimensions in every system of units.

Suppose:

[Q] = [MᵃLᵇTᶜ]

Then:

n₁u₁ = n₂u₂

The numerical value changes when the unit changes. The physical quantity remains the same.

For example:

1 newton = 1 kg m s⁻²

Using:

1 kg = 10³ g

1 m = 10² cm

Therefore:

1 N = 10³ × 10² g cm s⁻²

1 N = 10⁵ dyne

Limitations of Dimensional Analysis

Dimensional analysis cannot:

• Determine numerical constants such as 2, ½ or π.
• Distinguish between quantities having identical dimensions.
• Decide whether terms are added or subtracted.
• Derive equations containing trigonometric or exponential functions.
• Prove that a dimensionally correct equation is physically exact.
• Find a complete relation when too many variables are involved.

For example, work and torque have the same dimensions. Dimensional analysis cannot distinguish between them.

Units and Measurement Quick Revision Table

Important Terms from Chapter 1

Physical quantity: A measurable property expressed through a numerical value and a unit.

Unit: An accepted standard used to measure a physical quantity.

Fundamental quantity: An independent quantity that does not depend on other physical quantities.

Derived quantity: A quantity expressed through fundamental quantities.

Significant figures: Reliable digits and the first uncertain digit in a measured result.

Scientific notation: A method of writing numbers in the form a × 10ᵇ.

Dimension: The power of a base quantity in the representation of a physical quantity.

Dimensional formula: An expression showing a physical quantity through powers of base quantities.

Dimensional equation: An equation equating a physical quantity with its dimensional formula.

Principle of homogeneity: The rule that all terms in a valid physical equation have identical dimensions.

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