UNITS AND MEASUREMENTS
Class 11 Physics — Chapter 1
Detailed Study Notes • Worked Examples • Practice Questions • Answer
Key
Coverage: measurement, SI units, fundamental and derived units, scientific notation, significant figures,
accuracy and precision, errors, absolute/relative/percentage error, propagation of errors, dimensional
formulae, dimensional equations, unit conversion, applications and limitations of dimensional analysis.
How to use these notes: Read the concept → study the solved example → solve the practice questions without
looking at the answer → revise the formula box.
Class 11 Physics • Units and Measurements • Page 1
, 1. Physical Quantities and Measurement
Physical quantity: A physical quantity is a quantity that can be measured and expressed numerically together
with a unit. Examples: length, mass, time, temperature, velocity and force.
Measurement: Measurement is the comparison of an unknown physical quantity with an accepted standard of
the same kind.
A measurement is written as: Physical quantity = numerical value × unit.
Example: 5.2 m means the measured length is 5.2 times the standard metre.
Characteristics of a standard unit
A good standard should be well defined, invariable, easily reproducible, universally accepted and convenient
in magnitude.
Order of magnitude and scientific notation
Very large or very small measurements are conveniently written as a × 10ⁿ, where 1 ≤ a < 10. For example,
0.0000045 m = 4.5 × 10⁻⁶ m.
Solved Problem 1
Express 0.000072 km in metres.
Solution: 1 km = 10³ m. Therefore 0.000072 km = 0.000072 × 10³ m = 0.072 m.
Solved Problem 2
A runner completes 400 m in 50 s. Find average speed.
Solution: Average speed = distance/time = 400/50 = 8 m s⁻¹.
Practice
1. Express 0.00000031 m in scientific notation. 2. Convert 3.5 km to m. 3. A car travels 900 m in 45 s. Find its
average speed. 4. Convert 2.5 × 10⁶ mm into km.
Class 11 Physics • Units and Measurements • Page 2
Class 11 Physics — Chapter 1
Detailed Study Notes • Worked Examples • Practice Questions • Answer
Key
Coverage: measurement, SI units, fundamental and derived units, scientific notation, significant figures,
accuracy and precision, errors, absolute/relative/percentage error, propagation of errors, dimensional
formulae, dimensional equations, unit conversion, applications and limitations of dimensional analysis.
How to use these notes: Read the concept → study the solved example → solve the practice questions without
looking at the answer → revise the formula box.
Class 11 Physics • Units and Measurements • Page 1
, 1. Physical Quantities and Measurement
Physical quantity: A physical quantity is a quantity that can be measured and expressed numerically together
with a unit. Examples: length, mass, time, temperature, velocity and force.
Measurement: Measurement is the comparison of an unknown physical quantity with an accepted standard of
the same kind.
A measurement is written as: Physical quantity = numerical value × unit.
Example: 5.2 m means the measured length is 5.2 times the standard metre.
Characteristics of a standard unit
A good standard should be well defined, invariable, easily reproducible, universally accepted and convenient
in magnitude.
Order of magnitude and scientific notation
Very large or very small measurements are conveniently written as a × 10ⁿ, where 1 ≤ a < 10. For example,
0.0000045 m = 4.5 × 10⁻⁶ m.
Solved Problem 1
Express 0.000072 km in metres.
Solution: 1 km = 10³ m. Therefore 0.000072 km = 0.000072 × 10³ m = 0.072 m.
Solved Problem 2
A runner completes 400 m in 50 s. Find average speed.
Solution: Average speed = distance/time = 400/50 = 8 m s⁻¹.
Practice
1. Express 0.00000031 m in scientific notation. 2. Convert 3.5 km to m. 3. A car travels 900 m in 45 s. Find its
average speed. 4. Convert 2.5 × 10⁶ mm into km.
Class 11 Physics • Units and Measurements • Page 2
