Units And Measurements Class 11 Notes Physics Chapter 2 - CBSE

Chapter : 2

What Are Units And Measurements ?

Physical Quantity

The physical properties of a body that can be measured are known as physical quantities. Example: Length, mass, volume, temperature etc.


The quantity of a constant magnitude which is used to measure the magnitudes of the physical quantities.

Example : Unit of length is metre, unit of mass is kg, unit of velocity m/s-2 etc.

Fundamental unit

The units of the fundamental quantities are called fundamental units. Example: The fundamental unit of mass is kg, the fundamental unit of length is metre, the fundamental unit of time is second etc.

Derived unit

The units that are derived from the combination of the fundamental units are known as the derived units. Example: The derived unit of force kg.m/s, the derived unit of pressure kg.m–1.s–2 etc.

System of Units

The combination of fundamental units and derived units are known as system of units.

Types of Measuring Systems

  • CGS System
    • Centimetre, Gram and Second
  • FPS System
    • Foot, Pound and Second
  • MKS or SI System
    • Metre, kilogram and second



The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is known as error.

Least Count

The smallest value that can be measured by the measuring instrument is called its least count.

Actual Or True Value

The average of the measured values of a measurement is known as the actual value or true value.


Accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. Example : If the true value of gravitational acceleration is 9.8 m/s2 and the measured value is 9.7 or 9.8 m/s2 then it is accuracy of a measurement.


Precision is known as at what resolution or limit the quantity is measured.

Systematic Errors

  • Instrumental errors: The instrumental errors occur due to the imperfect design or calibration of the
    measuring unit.
  • Error in experimental techniques: Error in experimental techniques means the error in the measurement
    technique, experimental process.
  • Personal errors: Personal error is the error that arises due to the observer’ s fault. Personal error is the error like taking observations without observing proper precautions.
    • Parallax: The parallax error occurs due to the apparent position of the object angle for the viewing
      angle of the observer.
    • Remedy: The perpendicular viewing angle of the observer helps to prevent the parallax error.

Random Errors

The errors in measurement that lead to measurable values which are inconsistent when repeated measures of a constant attribute or quantity are taken.

  • Least count error: The least count error is the error associated with the resolution of the instrument.
  • Absolute error: The magnitude of the difference between the individual measurement and the true value of the quantity is called absolute error of measurement.
  • Relative error: The relative error is the ratio of the mean absolute error to the mean value of the quantity measured.
  • Percentage error: When the relative error is represented in percentage, it is known as percentage error.

Combination of Errors

  • Error of a sum or a difference: When two quantities are added or subtracted, the absolute error in the
    final result is the sum of the absolute errors in the individual quantities.
  • Error of a product or a quotient: When two quantities are multiplied or divided, the relative error in the result is the product of the relative errors in the multipliers.
  • Error in case of a measured quantity raised to a power: The relative error in a physical quantity raised to power k is the k times the relative error in the individual quantity.

Significant Figures

The reliable digits and the first uncertain digit are known as significant figures. Example: 2569, in this number there are 4 significant figures. 2,5,6 and 9 are the significant figures.

Rules for significant figures

  • Every non-zero number is significant.
  • Zero between numbers are significant.
  • Zeros at the right hand side of the decimal point after the non-zero numbers are significant.
  • Zeros at the initial position after the decimal point of the non-zero numbers are not significant.

Rules for arithmetic operations with significant figures

  • In multiplication or division, the final result should retain as many significant figures as there are in the original number with the least significant figures.
  • In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

Rounding Off

Rounding off is the rule by the convention that the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the letter is less than 5.

Dimension Of Physical Quantities

The dimensions of a physical quantity are the powers to which the base quantities are raised to represent that quantity.

Dimension Analysis

The principle of homogeneity of dimensions states that in any mathematical expression or equation involving physical quantities, each term in the expression or each term on either side of the equation must have the same dimension.

Dimensional formula

The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called dimensional formula.

Dimensional equation

An equation obtained by equating a physical quantity with its dimensional formula is called dimensional equation.

Application of dimensional analysis

  • Dimensional analysis helps to find out the unit of a physical quantity.
  • Dimensional analysis helps to find out dimensions of a constant.
  • Physical quantities can be expressed from one system to another with the help of dimensional analysis.