Original revision notes and practice for selected chapter concepts. Chapter sequence: PECTAA-listed English-medium Physics 9, revised NCP 2023. Not an official exercise key or an exam-session smart syllabus.

Physical quantities and SI units

Length, mass and time describe measurable properties. A measurement such as 2.4 m is meaningful because it gives both a numerical value and a standard unit. Base quantities are independent starting points; derived quantities combine them. Speed, for example, has unit m/s because it divides distance by time.

  • The SI base units are metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd).
  • Use symbols consistently: kg is a mass unit; N is a force unit.
  • Keep a space between a value and a unit symbol, such as 12 cm.

Powers of ten and unit conversions

Scientific notation writes a non-zero value as a number from 1 up to, but not including, 10 multiplied by a power of ten. Keep the unit attached. For a conversion, multiply by an equal ratio so the old unit cancels. Area and volume conversions require the conversion factor to be squared or cubed.

  • 2.4 km = 2.4 × 1000 m = 2400 m.
  • 0.000072 m = 7.2 × 10⁻⁵ m.
  • 1 cm² = (0.01 m)² = 0.0001 m².

Read the scale and check its zero

Choose an instrument with suitable range and resolution. Look squarely at an analogue scale to reduce parallax, and check its zero before measuring. For a stated direct vernier scale, add the main-scale reading to the coinciding vernier division multiplied by the least count.

  • Vernier reading = main-scale reading + coinciding division × least count.
  • For a screw gauge, least count = pitch ÷ number of circular-scale divisions.
  • Corrected reading = observed reading − signed zero error. A negative zero error therefore produces a positive correction.

Accuracy, precision and significant figures

Accuracy concerns closeness to the accepted value; precision concerns the spread of repeated readings. Repeating measurements can reveal random variation, but does not remove a constant zero error. Significant figures describe how a numerical result is reported; leading zeros locate the decimal point, while trailing zeros after a decimal can indicate measured precision.

  • 0.00450 has three significant figures: 4, 5 and the final 0.
  • Retain guard digits while calculating and round the final result appropriately.
  • When an uncertainty is supplied, report the value consistently with that uncertainty.

Worked examples

These are original SchoolOrbit examples. They are not numbered textbook exercises.

A vernier reading with zero correction

A direct vernier has a 0.1 mm least count. Its main-scale reading is 12 mm and division 6 coincides. The zero error is +0.2 mm. Find the corrected length.

  1. Vernier contribution = 6 × 0.1 mm = 0.6 mm.
  2. Observed length = 12 mm + 0.6 mm = 12.6 mm.
  3. Corrected length = 12.6 mm − (+0.2 mm) = 12.4 mm.

Result: 12.4 mm

A screw-gauge reading

A screw gauge advances 0.5 mm in one turn and has 50 circular divisions. The main scale reads 3.5 mm and the circular scale reads 24. Its zero error is −0.02 mm. Find the corrected thickness.

  1. Least count = 0.5 ÷ 50 = 0.01 mm.
  2. Observed thickness = 3.5 + 24 × 0.01 = 3.74 mm.
  3. Corrected thickness = 3.74 − (−0.02) = 3.76 mm.

Result: 3.76 mm

Try the original practice

Work out each answer first, then open the explanation. This page does not record answers or award an online score.

Practice 1

Convert 3.6 km to metres.

Show answer and explanation

3600 m

The kilometre is 1000 metres, so 3.6 × 1000 = 3600.

Practice 2

How many significant figures are written in 0.00620?

  1. Two
  2. Three
  3. Four
  4. Five
Show answer and explanation

Three

The leading zeros are placeholders. The digits 6, 2 and the final decimal zero are significant.

Practice 3

An instrument reads 8.6 mm with a +0.3 mm zero error. Find the corrected reading.

Show answer and explanation

8.3 mm

Subtract the signed zero error: 8.6 − (+0.3) = 8.3 mm.

Common mistakes to avoid

  • Converting cm² to m² using 0.01 instead of (0.01)².
  • Treating every zero in a number as a significant digit.
  • Adding a positive zero error instead of subtracting it.

Sources and scope

The chapter sequence is checked against the official directory and source book. The explanations, numerical values and practice are independently written for SchoolOrbit. No PECTAA endorsement, complete exercise key or examination-session coverage is claimed.

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