Class 9 · Physics · FBISE Islamabad

Chapter 1: Physical Quantities and Measurement

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Concept 2

Numerical 1

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Concept

1 3 mkConcept

What are base quantities and derived quantities? Give two examples of each.

DEFINE 1 Base quantities are those that cannot be expressed in terms of any other physical quantity — e.g. length and mass.

DEFINE 2 Derived quantities are obtained by combining base quantities — e.g. speed and force.

NOTE There are seven base quantities in the SI system.

Answer Base: length, mass. Derived: speed, force.

Common mistake

Give the examples with their units if the question asks for units — a mark is often attached to the unit.

3 4 mkConcept

Write 0.000045 m and 75,000 m in scientific notation and state the number of significant figures in each.

STEP 1 0.000045 m = 4.5 × 10⁻⁵ m — 2 significant figures.

STEP 2 75,000 m = 7.5 × 10⁴ m — 2 significant figures.

RULE In scientific notation one non-zero digit is written before the decimal point.

Answer 4.5 × 10⁻⁵ m (2 s.f.) and 7.5 × 10⁴ m (2 s.f.)

Common mistake

Leading zeros are never significant; trailing zeros in a plain whole number are ambiguous, which is why scientific notation is asked for.

Numerical

2 4 mkNumerical

The main scale of a vernier callipers reads 2.4 cm and the 6th vernier division coincides with a main-scale division. Find the length, given the least count is 0.01 cm.

Main scale = 2.4 cmVernier div = 6LC = 0.01 cmFind length

STEP 1 Vernier reading = division × least count

STEP 2 = 6 × 0.01 cm = 0.06 cm

STEP 3 Length = main scale + vernier reading

STEP 4 = 2.4 + 0.06 = 2.46 cm

Answer Length = 2.46 cm

Common mistake

Keep both decimal places. Writing 2.5 cm rounds away the precision the instrument was used for.

This sheet was checked against the FBISE Islamabad 2024 marking scheme.