page 1-6 course book unit 1.1 …Quantities and measurement techniquesMeasurement Techniques

Measurements use the SI system (decimal, based on length, mass, time). Powers of ten provide compact notation for large/small numbers (e.g., $4000 = 4 \times 10^{3}$ , $0.004 = 4 \times 10^{-3}$ ). Standard notation aids quick magnitude comparison.

The SI unit of length is the metre (m). Common submultiples: $1\text{ cm} = 10^{-2} \text{ m}$ , $1\text{ mm} = 10^{-3} \text{ m}$ ; large distances: $1\text{ km} = 10^{3} \text{ m}$ . Avoid parallax error when reading rulers by viewing directly over the mark; readings are to the nearest subunit.

Measurements have uncertainty. Significant figures (s.f.) indicate precision (e.g., $4.5$ has two s.f., $0.0385$ has three s.f.). Calculation results should match the least precise measurement's s.f. (e.g., $3.4185062$ becomes $3.4$ for two s.f., $3.42$ for three s.f.). Round using the next digit.

Area formulas: Triangle ( $A<em>{\triangle} = \tfrac{1}{2} \times \text{base} \times \text{height}$ ), Circle ( $A</em>{\odot} = \pi r^{2}$ ), Square/rectangle ( $A = \text{length} \times \text{breadth}$ ). Area unit: $\text{m}^{2}$ ( $1\ \text{cm}^{2} = 10^{-4} \ \text{m}^{2}$ ). Volume formulas: Rectangular block ( $V = \text{length} \times \text{breadth} \times \text{height}$ ), Cylinder ( $V = \pi r^{2} h$ ). Volume units: $1\ \text{cm}^{3} = 1\ \text{mL}$ ; $1\ \text{L} = 1000\ \text{cm}^{3}$ ; $1\ \text{m}^{3} = 1000\ \text{L}$ . Convert as needed.

The second (s) is defined by caesium atomic transitions. Clocks use constant oscillations. For accurate time measurement, select an appropriate timer. For periodic motion, time multiple oscillations and average the period to reduce error. Frequency $f = \frac{1}{T}$ .

Vectors have magnitude and direction; scalars have only magnitude. For perpendicular vectors $A$ and $B$ , the resultant magnitude is $R = \sqrt{A^{2} + B^{2}}$ .