Measurement & Unit Conversion Essentials

Comparing Measurable Properties

  • Length, mass, volume, and height are quantifiable and allow direct comparison between objects.

  • Consistent units are required before comparing magnitudes.

Measurement Basics

  • Measurement = numerical value + unit (e.g.
    length=5 cm\text{length}=5\,\text{cm}).

  • Provides a standardized, precise description of physical properties.

International System of Units (SI)

  • Global metric‐based standard; decimal relationships.

  • Seven fundamental quantities/units:

    • Mass – kilogram (kg)

    • Length – metre (m)

    • Time – second (s)

    • Electric current – ampere (A)

    • Temperature – kelvin (K)

    • Amount of substance – mole (mol)

    • Luminous intensity – candela (cd)

Derived Units & Prefixes

  • Derived by multiplying/dividing base units (e.g. area m2\text{m}^2, volume m3\text{m}^3, speed m s−1\text{m}\,\text{s}^{-1}).

  • Common prefixes indicate powers of 1010 (kilo 10310^3, centi 10−210^{-2}, milli 10−310^{-3}, micro 10−610^{-6}, etc.).

Unit Conversion (Factor-Label Method)

  • Steps:

    1. Identify given and desired units.

    2. Choose appropriate conversion factor(s).

    3. Arrange so desired unit is in the numerator; unwanted units cancel.

    4. Multiply/divide to compute result.

  • Larger → smaller unit: move decimal right / multiply.

  • Smaller → larger unit: move decimal left / divide.

Accuracy vs Precision

  • Accuracy: closeness to the true value.

  • Precision: closeness of repeated measurements to one another.

  • Data can be precise but inaccurate (systematic error) or accurate but imprecise (random error).

Density

  • Definition: mass per unit volume.
    ρ=mV\rho = \frac{m}{V}

  • Units: g cm−3\text{g}\,\text{cm}^{-3} or kg m−3\text{kg}\,\text{m}^{-3}.

  • Less dense objects float on more dense fluids (e.g. oil on water).

  • To find an unknown:

    • Mass known: V=mρV = \frac{m}{\rho}.

    • Volume known: m=Vρm = V\rho.

  • Volume measurement:

    • Regular solids – geometric formulas.

    • Irregular solids – water displacement.