AFNS Physics Chapter 01# Measurements

1:Physical Quantities and SI Units

In Physics, every measurement has two parts: a number and a unit. For example, if someone says ‘the table is 2 metres long’ — 2 is the number and metre is the unit. Without units, a measurement is meaningless.

1.1 Types of Physical Quantities

KEY CONCEPT:  Physical quantities are divided into two types: Base Quantities (7 fundamental quantities) and Derived Quantities (formed by combining base quantities).

Base Quantities

These are the fundamental quantities that cannot be expressed in terms of other quantities. There are exactly 7 SI base quantities:

QUICK TIP:  In AFNS MCQs the most common trick is mixing up units. Remember: kilogram is for MASS (not weight), kelvin is for TEMPERATURE (not Celsius), candela is for LUMINOUS INTENSITY.

Derived Quantities

These are obtained by combining base quantities through multiplication or division. You do NOT need to memorise them separately — just know the formula.

EXAMPLE:  Force has SI unit Newton. Newton = kg·m/s². So if asked ‘What are the base units of Force?’ the answer is kg·m·s⁻².

2. Scientific Notation and SI Prefixes

In Physics we deal with very large numbers (like the speed of light = 300,000,000 m/s) and very small numbers (like electron mass = 0.00000000000000000000000000000091 kg). Scientific notation makes these easy to write and compare.

2.1 Scientific Notation

KEY CONCEPT:  Scientific notation: A × 10ⁿ, where 1 ≤ A < 10 and n is a positive or negative integer.

EXAMPLE:  Speed of light = 3.0 × 10⁸ m/s    |    Electron mass = 9.1 × 10⁻³¹ kg    |    Diameter of atom = 1.0 × 10⁻¹⁰ m

2.2 SI Prefixes (Must Memorize)

Instead of writing 10⁻³ every time, we use prefixes like milli (m). These are extremely important for AFNS MCQs.

QUICK TIP:  Memory trick for order: ‘The Great Man Keeps His Desk Clean Making Nice Pots’ = Tera, Giga, Mega, Kilo, Hecto, Deca, Centi, Milli, Nano, Pico

3. Significant Figures

Significant figures (sig figs) show how precise a measurement is. Every digit that is reliably known plus one uncertain digit is significant.

3.1 Rules for Counting Significant Figures

• All non-zero digits are significant. Example: 4567 → 4 sig figs
• Zeros between non-zero digits are significant. Example: 4007 → 4 sig figs
• Leading zeros are NOT significant. Example: 0.0045 → 2 sig figs
• Trailing zeros AFTER a decimal point are significant. Example: 3.400 → 4 sig figs
• Trailing zeros in a whole number are ambiguous unless a decimal point is shown. Example: 500 → unclear; 500. → 3 sig figs

EXAMPLE:  How many sig figs in 0.0050300?  Answer: 5  (leading zeros don’t count; 5, 0, 3, 0, 0 after the first non-zero digit are all significant)

3.2 Calculations with Significant Figures

KEY CONCEPT:  Addition/Subtraction: Round answer to fewest DECIMAL PLACES.   Multiplication/Division: Round answer to fewest SIGNIFICANT FIGURES.

EXAMPLE:  Addition: 12.5 + 1.234 = 13.734 → round to 1 decimal place → 13.7     |     Multiplication: 4.5 × 2.34 = 10.53 → 2 sig figs → 11

QUICK TIP:  AFNS shortcut: In division/multiplication questions, always count sig figs in each given value. Your answer cannot be more precise than your least precise measurement.

3.3 Rounding Rules

• If the digit to be dropped is less than 5 → round down (keep previous digit same)
• If the digit to be dropped is 5 or more → round up (increase previous digit by 1)

EXAMPLE:  Round 3.465 to 2 decimal places: digit after 6 is 5 → round up → 3.47

4. Errors in Measurements

No measurement is 100% perfect. The difference between the measured value and the true value is called error. Understanding errors is essential for accurate scientific work.

4.1 Types of Errors

(a) Systematic Errors

These errors always push the result in the same direction — always too high or always too low. They are caused by faults in the instrument or method.

• Zero error in instruments (e.g., a ruler that does not start from exactly zero)
• Poorly calibrated instruments
• Environmental effects (e.g., temperature affecting a metal ruler)

KEY CONCEPT:  Systematic errors cannot be reduced by repeating the experiment. They must be identified and corrected.

(b) Random Errors

These errors are unpredictable and can push the result either too high or too low. They are caused by limitations of the measuring instrument or the observer.

• Observer’s reaction time in timing experiments
• Parallax error while reading a scale
• Slight variations in experimental conditions

KEY CONCEPT:  Random errors can be reduced by repeating the experiment many times and taking the average (mean) of readings.

4.2 Accuracy vs Precision

QUICK TIP:  Classic AFNS question: ‘A student gets 9.8, 9.7, 9.9 for g but true value is 9.81 — is this accurate or precise?’ Answer: Both accurate AND precise!

4.3 Absolute, Relative and Percentage Error

• Absolute Error = |Measured Value − True Value|
• Relative Error = Absolute Error / True Value
• Percentage Error = Relative Error × 100%

EXAMPLE:  True value of g = 9.81 m/s², Measured value = 9.75 m/s²   |   Absolute error = |9.75 − 9.81| = 0.06   |   Percentage error = (0.06/9.81) × 100 = 0.61%