Measurements and Experimentation

The One Thing

A physical measurement is meaningful only when it includes both a numerical value and an appropriate unit. Reliable experimentation depends on suitable instruments, correct technique, controlled variables, careful recording, error analysis, safe practice, and conclusions supported by evidence.

Reactions, Processes and Experiments

Key Terms

• Physical quantity: A property that can be measured and expressed with a number and a unit, such as length, mass, or time.
• Unit: A fixed standard used for measuring a physical quantity.
• SI system: The internationally accepted system of units used in science.
• Fundamental quantity: A basic physical quantity that is independent of other quantities, such as length, mass, and time.
• Derived quantity: A quantity obtained by combining fundamental quantities, such as speed, area, volume, and density.
• Least count: The smallest measurement that an instrument can read reliably.
• Accuracy: How close a measured value is to the true or accepted value.
• Precision: How closely repeated measurements agree with one another.
• Error: The difference between a measured value and the true or accepted value.
• Parallax error: An error caused by viewing a scale from an angle instead of keeping the eye directly above the reading.
• Zero error: An error present when an instrument does not read zero when it should.
• Significant figures: The meaningful digits in a measured value, including all certain digits and the first uncertain digit.
• Observation: Information obtained by using the senses or measuring instruments during an experiment.
• Hypothesis: A testable proposed explanation or prediction about an observation.
• Variable: A quantity that may change during an experiment.
• Independent variable: The quantity deliberately changed by the experimenter.
• Dependent variable: The quantity measured or observed in response to the independent variable.
• Control variable: A quantity kept constant to make the experiment fair.
• Density: Mass per unit volume of a substance.
• Scientific notation: A convenient way of writing very large or very small numbers in the form a × 10^n, where 1 ≤ a < 10.

Easily Confused

• Accuracy and precision: Accuracy concerns closeness to the true or accepted value; precision concerns agreement between repeated measurements.
• Fundamental and derived quantities: Fundamental quantities are independent basic quantities; derived quantities are formed by combining fundamental quantities.
• Independent and dependent variables: The independent variable is deliberately changed; the dependent variable is measured in response.
• Control variable and independent variable: The independent variable changes during the experiment; a control variable is kept constant.
• Parallax error and zero error: Parallax error results from viewing a scale from an angle; zero error exists when an instrument fails to read zero when it should.
• Lower and upper meniscus readings: The lower meniscus is read for water and most liquids; the upper meniscus is read for mercury.
• Mean and accepted value: The mean is calculated from repeated readings; the accepted value is the true or established value used for comparison.
• Area, volume, speed and density: Area is measured in square metre (m²), volume in cubic metre (m³), speed in metre per second (m/s), and density in kilogram per cubic metre (kg/m³).

What Gets Asked

• Writing measurements correctly: Questions may require a numerical value and a unit. Omitting the unit makes the measurement incomplete.
• Selecting SI units and conversions: Questions may test the seven SI base quantities and conversions such as 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 hour = 3600 s, and 1 litre = 1000 cm³ = 10^-3 m³. Marks are lost through incorrect conversion factors or unit symbols.
• Calculating derived quantities: Problems may involve Speed = distance ÷ time, Density = mass ÷ volume, or geometrical volume formulae. The relevant equation must be used with consistent units.
• Reading instruments and measuring volume: Questions may test ruler readings, damaged zero marks, water displacement, eye-level readings, and the correct meniscus. The main errors are failing to subtract an initial reading, reading from an angle, or using the wrong meniscus.
• Analysing repeated measurements and errors: Questions may require mean = sum of readings ÷ number of readings, absolute error, or percentage error = (absolute error ÷ accepted value) × 100. A common mistake is confusing precision with accuracy.
• Designing or evaluating an experiment: Questions may ask for the independent, dependent, and control variables, graph requirements, experimental-record sections, precautions, or sources of error. Marks are lost when control variables are not kept unchanged, observations are not recorded honestly, or results are reported with unjustified significant figures.