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.
  \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 \text{m}^2, volume \text{m}^3, speed \text{m}\,\text{s}^{-1}).

• Common prefixes indicate powers of 10 (kilo 10^3, centi 10^{-2}, milli 10^{-3}, micro 10^{-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.
  \rho = \frac{m}{V}

• Units: \text{g}\,\text{cm}^{-3} or \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 = \frac{m}{\rho}.

  • Volume known: m = V\rho.

• Volume measurement:

  • Regular solids – geometric formulas.

  • Irregular solids – water displacement.