Physical Quantities & Measurement

Class 9 Physics — Federal Board (FBISE)

1. Physical Quantities

A physical quantity is any quantity that can be measured. All physical quantities have two parts: a numerical value and a unit.

• Base quantities: fundamental quantities that cannot be expressed in terms of other quantities — length, mass, time, temperature, electric current, luminous intensity, amount of substance.
• Derived quantities: quantities obtained by combining base quantities — speed, area, volume, force, density.

2. International System of Units (SI)

The SI system is the internationally agreed system of units used in science worldwide.

• 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)

3. Prefixes

Prefixes are used with SI units to express very large or very small quantities:

• Giga (G) = 10⁹
• Mega (M) = 10⁶
• Kilo (k) = 10³
• Centi (c) = 10⁻²
• Milli (m) = 10⁻³
• Micro (μ) = 10⁻⁶
• Nano (n) = 10⁻⁹

4. Scientific Notation

A method of writing very large or very small numbers in the form A × 10ⁿ, where A is a number between 1 and 10.

• Example: 5,000,000 m = 5 × 10⁶ m
• Example: 0.000003 m = 3 × 10⁻⁶ m

5. Measuring Instruments

• Metre rule — measures length up to 1 m, least count = 1 mm
• Vernier calliper — measures small lengths, least count = 0.1 mm
• Micrometre screw gauge — measures very small lengths, least count = 0.01 mm
• Physical balance — measures mass
• Stopwatch — measures time intervals

6. Vernier Calliper

A vernier calliper has two scales — a main scale and a vernier scale. The reading is calculated as:

Reading = Main scale reading + (Vernier scale division × Least count)

Least count of vernier calliper = 1 MSD − 1 VSD = 0.1 mm

7. Micrometre Screw Gauge

Used to measure the diameter of thin wires and small spheres. It has a thimble scale and a main scale.

Reading = Main scale reading + (Thimble scale reading × Least count)

Least count = 0.01 mm

8. Errors in Measurement

• Systematic error: consistent error due to faulty instruments or poor technique — always in the same direction.
• Random error: unpredictable error that varies — reduced by taking multiple readings and averaging.
• Zero error: error when an instrument does not read zero when it should — can be positive or negative.

9. Significant Figures

Significant figures are the meaningful digits in a measurement that carry certainty plus one estimated digit.

• All non-zero digits are significant: 345 has 3 significant figures.
• Zeros between non-zero digits are significant: 3005 has 4 significant figures.
• Trailing zeros after a decimal point are significant: 3.50 has 3 significant figures.
• Leading zeros are NOT significant: 0.0045 has 2 significant figures.

Summary

• Physical quantities = base + derived; all require a unit.
• SI has 7 base units; learn their names and symbols.
• Use prefixes and scientific notation for very large/small values.
• Vernier calliper (0.1 mm) and screw gauge (0.01 mm) give precise measurements.
• Always account for zero error and reduce random error by repeating readings.
• Report answers with correct significant figures.