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Topic 01 of 11

Measurement

SI UnitsScalars & VectorsSig FigsPercentage Error
Table of six SI base units on the left and scalar versus vector comparison on the right SI Base Units Scalar vs Vector Quantity Unit (symbol) Lengthmetre (m)Masskilogram (kg)Timesecond (s)Temperaturekelvin (K)Currentampere (A)Amountmole (mol) Scalar Vector SpeedVelocityDistanceDisplacementMassWeightTimeForceEnergyAccelerationTemperatureMomentum Magnitude only Magnitude + direction
SI Base Units and Scalar vs Vector Quantities

Contents

  1. SI base units
  2. Scalars and vectors
  3. Measuring instruments
  4. Significant figures
  5. Percentage error
  6. Common exam traps
Topic 1 of 12
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1. SI Base Units

Every physical quantity has a standard unit. The seven SI base units are the foundation — all derived units (like N, J, W) come from combinations of these.

QuantityUnitSymbol
Lengthmetrem
Masskilogramkg
Timeseconds
TemperaturekelvinK
Electric currentampereA
Amount of substancemolemol

Common prefixes

PrefixSymbolMultiplier
millim× 10⁻³ (e.g. 500 mA = 0.5 A)
centic× 10⁻² (e.g. 25 cm = 0.25 m)
kilok× 10³ (e.g. 2 km = 2000 m)
megaM× 10⁶ (e.g. 5 MHz = 5×10⁶ Hz)
Exam tip

Always convert to SI base units before substituting into a formula. 5 cm → 0.05 m; 200 g → 0.2 kg; 3 ms → 0.003 s.

2. Scalars and Vectors

Scalar quantity

Has magnitude (size) only — fully described by a number and unit.

Vector quantity

Has both magnitude and direction — must include a number, unit, and direction to be complete.

ScalarsVectors
DistanceDisplacement
SpeedVelocity
MassWeight / Force
Energy, Work, PowerAcceleration
Temperature, TimeMomentum
Common mistake

"Speed is 10 m/s east" — wrong. Speed is scalar, it has no direction. Correct term is velocity: "velocity is 10 m/s east". This is a frequent 1-mark trap.

3. Measuring Instruments

InstrumentMeasuresPrecision
Metre ruleLength1 mm
Vernier callipersLength0.1 mm
Micrometer screw gaugeSmall length0.01 mm
Stopwatch (digital)Time0.01 s
ThermometerTemperature1 °C (typical)

Parallax error occurs when your eye is not perpendicular to the scale — the reading looks different from different angles. Always read at eye level, directly in line with the scale marking.

Practical tip

For a liquid in a tube, read the bottom of the meniscus at eye level to avoid parallax error.

4. Significant Figures

Worked example

How many significant figures in 0.04560 m?

Leading zeros are not significant. Digits 4, 5, 6, 0 are all significant. Answer: 4 significant figures.

Rule

Give your final answer to the same number of significant figures as the least precise measurement given. Only round at the final step — not mid-calculation.

5. Percentage Error

% error = (absolute error ÷ measured value) × 100%Absolute error = smallest scale division of the instrument
Worked example

A metre rule (smallest division 1 mm) measures a length of 0.50 m. Find the percentage error.

% error = (0.001 ÷ 0.50) × 100% = 0.2%

Random vs systematic error

Random errorSystematic error
Varies unpredictably each readingConsistent — same direction every time
Reduced by taking more repeats and averagingCannot be fixed by repeating — must be identified
Example: reaction time when pressing stopwatchExample: zero error on a balance
Reducing timing error

Time 20 complete oscillations and divide by 20. This reduces the percentage error in each period by a factor of 20 compared to timing a single swing.

Must-Know for Exam

6. Common Exam Traps

Trap 1 — Missing units

Always write the unit in every numerical answer. "The length is 0.25" scores zero. "The length is 0.25 m" scores the mark.

Trap 2 — Distance vs displacement

Distance is total path length (scalar). Displacement is the straight-line distance from start to finish in a specified direction (vector). A runner who completes a 400 m lap has distance 400 m but displacement 0 m.

Trap 3 — Zero error on instruments

Before using a micrometer or vernier calliper, check the zero reading when fully closed. If it reads 0.02 mm, subtract 0.02 mm from every measurement taken.

Key Terms — Flashcard Review

Tap each card to reveal the definition.

SI base units
Length: metre (m). Mass: kilogram (kg). Time: second (s). Current: ampere (A). Temperature: kelvin (K).
Scalar quantity
Has magnitude only. Examples: speed, distance, mass, time, temperature, energy.
Vector quantity
Has magnitude AND direction. Examples: velocity, displacement, force, acceleration, momentum.
Precision vs accuracy
Precision: repeated readings close together (low random error). Accuracy: readings close to true value (low systematic error).
Significant figures
All non-zero digits + zeros between them or after decimal. e.g. 0.0305 has 3 sig figs.
Zero error
Systematic error where instrument reads non-zero when measuring nothing. Must be subtracted from all readings.

🎯 Practice Quiz — Test Yourself

8 O Level-style questions on this topic. Select an answer to see instant feedback.

Question 1 of 8
A student measures 10.0 cm using a ruler. The uncertainty is ±1 mm. What is the percentage uncertainty?
Explanation: Percentage uncertainty = (0.1 cm / 10.0 cm) × 100% = 1%. Always convert units before dividing.
Question 2 of 8
Which instrument measures the diameter of a wire most accurately?
Explanation: Vernier calipers can measure to 0.1 mm. A micrometer screw gauge (0.01 mm) is even more precise.
Question 3 of 8
A result is precise but not accurate. This means the results are:
Explanation: Precision = results cluster together (repeatable). Accuracy = results are close to the true value. These are independent properties.
Question 4 of 8
Which of the following is a vector quantity?
Explanation: Velocity has both magnitude and direction — it is a vector. Speed, distance, and mass are scalars (magnitude only).
Question 5 of 8
A stopwatch reads 3.45 s then 7.20 s. What time interval was recorded?
Explanation: Time interval = 7.20 − 3.45 = 3.75 s. Subtract readings — do not add them.
Question 6 of 8
Which of the following is a vector quantity?
Explanation: Vectors have magnitude AND direction. Acceleration (change in velocity per unit time) has a direction. Speed, mass, and temperature are scalars - they have magnitude only.
Question 7 of 8
A student measures a length five times and gets very similar results, but all readings are 2 cm above the true value. This indicates:
Explanation: High precision = repeated readings are close together (consistent). Low accuracy = readings are far from the true value. This is a systematic error (e.g. zero error or incorrect calibration).
Question 8 of 8
The reading 0.00470 m has how many significant figures?
Explanation: Leading zeros are NOT significant. The significant figures in 0.00470 are 4, 7, and 0 (the trailing zero after the 7 IS significant because it follows a non-zero digit after a decimal point). So 3 significant figures.
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