Chapter 01 • Measurement

Measurement – The Foundation of Science

Learn the meaning of measurement, systems of units, SI units, and conversion between units with practical activities.

01

Measurement

Understand measurement as comparison of an unknown quantity with a known standard quantity of the same kind.

02

Systems of Units

Study CGS, FPS and MKS systems and understand why a common system of units became necessary.

03

SI Units

Learn the seven SI base units, their symbols and the advantages of the International System of Units.

04

Unit Conversion

Convert measurements between units while keeping the magnitude of the physical quantity unchanged.

What You Will Learn

Measurement is fundamental to science because physical quantities must be expressed using a numerical value and a unit. The chapter begins with practical measurement activities, then introduces different systems of units, the need for a common system, SI units and unit conversion.

$$\color{#0284c7}{Q} = \color{#059669}{n_1} \color{#7c3aed}{u_1} = \color{#059669}{n_2} \color{#7c3aed}{u_2}$$
$$\color{#059669}{n_2} = \color{#059669}{n_1} \left( \frac{\color{#7c3aed}{u_1}}{\color{#7c3aed}{u_2}} \right)$$
Q Physical Quantity (Constant)
n₁, n₂ Numerical Values
u₁, u₂ Measurement Units
Key idea: The physical quantity Q remains constant even when the unit u changes. A larger unit produces a smaller numerical value n, while a smaller unit produces a larger numerical value.

Measurement – The Foundation of Science: Concepts

1.1 Introduction: What is Measurement?

Measurement is the process of comparing an unknown quantity with a known standard quantity of the same kind. Physics is based on measurement. Whether we measure the length of a classroom, the mass of a bag, or the time taken by a runner, accurate measurement is essential.

Examples

  • A tailor measures cloth in metres.
  • A doctor measures body temperature in degree Celsius.
  • A shopkeeper measures rice in kilograms.

Without proper units, these measurements would have no meaning.

Activity 1.1

Measuring the Area of the Classroom Floor

Materials: Three sticks of lengths $l_1:l_2:l_3=1:2:3$.

Procedure:

  1. Divide students into 3 groups and hand over one stick to each group.
  2. Each group measures the length and width of the classroom using the stick as one unit.
  3. Compare the measured length, breadth and area using the three sticks.
Measurement Stick 1 Stick 2 Stick 3
Length of wall _____ units _____ units _____ units
Breadth of wall _____ units _____ units _____ units
Area of floor _____ units² _____ units² _____ units²

The activity demonstrates that the numerical value of a quantity is inversely proportional to the size of the unit used.

$$\color{#0284c7}{Q} = \color{#059669}{n_1} \color{#7c3aed}{u_1} = \color{#059669}{n_2} \color{#7c3aed}{u_2}$$
$$\color{#059669}{n_2} = \color{#059669}{n_1} \left( \frac{\color{#7c3aed}{u_1}}{\color{#7c3aed}{u_2}} \right)$$
Q Length / Area (Constant)
n₁, n₂ Number of Stick Units Counted
u₁, u₂ Stick Unit Length
Physical Length of Measured Wall (Constant Invariant Size Q) Stick 1 (Small Unit u₁ → Count n₁ = 6) Unit u₂ (Length 1) Unit u₂ (Length 2) Stick 2 (Large Unit u₂ → Count n₂ = 2)
Figure 1.1: Visual proof of $Q = n_1u_1 = n_2u_2$. Tripling unit size reduces numerical count to one-third.
Activity 1.2

Let's Play an Estimation Game

  1. Estimate the length of the blackboard without measuring.
  2. Measure its length using a metre scale.
  3. Compare the estimated and measured values and calculate the inaccuracy (error).

1.2 Different Systems of Units

In earlier times, different regions and places used their own units of measurement, which often led to confusion and errors.

(a) CGS System

  • Length: centimetre (cm)
  • Mass: gram (g)
  • Time: second (s)

It is mainly used in laboratory and scientific calculations.

(b) FPS System

  • Length: foot (ft)
  • Mass: pound (lb)
  • Time: second (s)

It is commonly used in the United States.

(c) MKS System

  • Length: metre (m)
  • Mass: kilogram (kg)
  • Time: second (s)

This system later developed into the SI system.

Example: The height of a person is largely measured in centimetres in India, while in some countries it is measured in feet and inches.

1.3 Need for a Common System of Units

Different systems of units caused difficulties in communication, trade and scientific research.

Problems Without a Common System

  • Confusion in international trade
  • Errors in scientific calculations
  • Difficulty in sharing scientific data
Example: If a scientist in India measures length in metres and another scientist in the USA measures in feet, comparison becomes difficult unless a common unit is used.
Activity 1.3

Let's Compare

Materials: Ruler marked in cm and inches.

  1. Measure the length of a book using both cm and inches.
  2. Compare the values and find the relation between them.

1.4 International System of Units (SI)

The International System of Units (SI) is the modern and universally accepted system of measurement.

SI Base Units

Physical Quantity SI Unit Symbol
Length metre m
Mass kilogram kg
Time second s
Temperature kelvin K
Electric current ampere A
Luminous intensity candela cd
Amount of substance mole mol

Advantages of SI Units

  • Internationally accepted
  • Easy to use and understand
  • Based on the decimal system
Examples: Speed of vehicles is measured in m/s or km/h; medicines are measured in milligrams (mg).

1.5 Conversion of Units Between Different Systems

Sometimes, we need to convert a measurement from one unit to another to ensure comprehension across different systems.

During unit conversion, the numerical value and the unit may change, but the magnitude of the physical quantity remains the same.

Basic Conversions

  • $1\,km=1000\,m$
  • $1\,m=100\,cm$
  • $1\,kg=1000\,g$
  • $1\,hour=3600\,s$

Example: Convert 9 km/h into m/s

$$9\,\frac{km}{h}=9\times\frac{1000\,m}{3600\,s} =\frac{5}{2}\,m/s$$

Example: Convert 1 N into g·cm/s²

$$1\,N=1\,kg\,m/s^2 =1000\,g\times100\,cm/s^2 =10^5\,g\,cm/s^2$$ $$1\,N=10^5\,dyne$$

Exercise 1.1 – Measurement: The Foundation of Science

The following questions are reproduced from the supplied chapter content. Answer reveals are provided where the answer can be directly established from the supplied material.

Question 1. Name any two systems of units.
View Answer

Any two: CGS, FPS or MKS.

Question 2. Why is SI system preferred over other systems?
View Answer

It is internationally accepted, easy to use and understand, and based on the decimal system.

Question 3. Convert 250 N into g·cm/s².
View Answer

$1\,N=10^5\,g\,cm/s^2$.

Therefore, $250\,N=250\times10^5=2.5\times10^7\,g\,cm/s^2$.

Question 4. Convert 1000 kg/L into kg/m³.
View Answer

Since $1\,L=10^{-3}\,m^3$,

$1000\,kg/L=1000\times1000=10^6\,kg/m^3$.

Question 5. Which of the following is not an SI unit?

(a) Meter   (b) Kilogram   (c) Second   (d) foot

View Answer

(d) foot

Question 6. The SI unit of mass is:

(a) Gram   (b) Kilogram   (c) Pound   (d) tonne

View Answer

(b) Kilogram

Question 7. Name the system of units used internationally.
View Answer

The International System of Units (SI).

Question 8. Why is a common system of units necessary?
View Answer

Different systems can cause confusion in international trade, errors in scientific calculations and difficulty in sharing scientific data.

Question 9. Why is measurement necessary in physics?
View Answer

Physics is based on measurement, and accurate measurement is essential for describing physical quantities.

Question 10. Why was there a need for a common system of units?
View Answer

Different systems of units created difficulties in communication, trade and scientific research.

Question 11. Explain the relation: Magnitude = Numerical value × Unit.
View Answer

The measured physical quantity can be represented as the product of its numerical value and its unit.

$$Q=n\times u$$
Question 12. Why does the same classroom floor give different numerical values when measured with sticks of different lengths?
View Answer

The numerical value is inversely proportional to the size of the unit. A longer stick gives a smaller numerical value, while a shorter stick gives a larger numerical value.

Question 13. In Activity 1.1, why are numerical values different?
View Answer

Because the three sticks have different lengths and therefore represent different unit sizes.

Question 14. Is the actual size of the classroom different? Why or why not?
View Answer

No. The physical size remains the same; only the numerical value changes because the unit changes.

Question 15. What conclusion can you draw about units and measurement from Activity 1.1?
View Answer

The physical quantity remains constant, while its numerical value depends on the size of the unit used.

Question 16. Fill in the blanks.
  1. Measurement is the process of comparing an unknown quantity with a ______ quantity.
  2. The SI unit of mass is ______.
  3. In CGS system, the unit of length is ______.
  4. $1\,km=$ ______ m.
  5. The modern internationally accepted system of units is called ______.
View Answers

(a) known   (b) kilogram   (c) centimetre   (d) 1000   (e) SI system / International System of Units

Question 17. Match the following.
Column A Column B
CGS Kelvin
FPS Pound
SI International system
MKS Meter-Kilogram-Second
View Answer

FPS → Pound; SI → International system; MKS → Meter-Kilogram-Second. The supplied matching list places Kelvin alongside CGS, but Kelvin is an SI unit of temperature, not a CGS base unit.

Question 18. What problems might occur if every country used its own system of units for measurement?
View Answer

Confusion in international trade, errors in scientific calculations and difficulty in sharing scientific data.

Question 19. A scientist measures length in feet and another in metres. What difficulties may it lead to?
View Answer

Direct comparison becomes difficult unless the measurements are converted to a common unit.

Question 20. If 1 metre was defined differently in different countries, what would happen to international trade?
View Answer

Measurements of goods would not have a common meaning, creating confusion and errors in international trade.

Question 21. A shopkeeper sells rice using kilograms. A foreign customer asks for rice in pounds.
  1. Why is unit conversion necessary here?
  2. If $1\,kg=2.2$ pounds, how many pounds are there in 5 kg?
View Answer

(a) Unit conversion is necessary because the shopkeeper and customer are using different units for the same physical quantity.

(b) $5\times2.2=11$ pounds.

Measurement Worksheets – Class 9 Advanced Science

Worksheets

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Measurement – Quick Revision Notes

Key Definitions

Concept Quick Revision
Measurement Comparing an unknown quantity with a known standard quantity of the same kind.
CGS Centimetre–gram–second.
FPS Foot–pound–second.
MKS Metre–kilogram–second.
SI International System of Units; the modern universally accepted system.
Physical quantity Its magnitude is represented through numerical value × unit.

SI Base Units

Quantity Unit Symbol
Length metre m
Mass kilogram kg
Time second s
Temperature kelvin K
Electric current ampere A
Luminous intensity candela cd
Amount of substance mole mol

Important Conversions

$$1\,km=1000\,m$$
$$1\,m=100\,cm$$
$$1\,kg=1000\,g$$
$$1\,hour=3600\,s$$

Core Measurement Relation

$$\color{#0284c7}{Q} = \color{#059669}{n} \color{#7c3aed}{u}$$
$$\color{#0284c7}{Q} = \color{#059669}{n_1}\color{#7c3aed}{u_1} = \color{#059669}{n_2}\color{#7c3aed}{u_2}$$
Q Physical Quantity
n, n₁, n₂ Numerical Value (Count)
u, u₁, u₂ Unit of Measurement

Measurement – Topic Tests

Interactive Tests

Test content was not supplied in the source material. This tab is reserved for graded topic tests covering measurement, systems of units, SI units and unit conversion.

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