ME-01: Units, Measurements & Errors
│
├── SI System
│   ├── 7 Base Quantities
│   │   ├── Length — metre (m) — [L]
│   │   ├── Mass — kilogram (kg) — [M]
│   │   ├── Time — second (s) — [T]
│   │   ├── Current — ampere (A)
│   │   ├── Temperature — kelvin (K)
│   │   ├── Amount — mole (mol)
│   │   └── Luminosity — candela (cd)
│   └── Derived Units
│       ├── Newton = kg m $s^{-2}$
│       ├── Joule = kg $m^{2}$ $s^{-2}$
│       ├── Pascal = kg $m^{-1}$ $s^{-2}$
│       └── Watt = kg $m^{2}$ $s^{-3}$
│
├── Dimensional Analysis
│   ├── Purpose
│   │   ├── Check equation correctness
│   │   ├── Derive unknown relationships
│   │   └── Convert between unit systems
│   ├── Method
│   │   ├── Express as M^a L^b T^c
│   │   └── Match exponents on both sides
│   └── Limitations
│       ├── Cannot find dimensionless constants
│       └── Cannot distinguish same-dimension formulas
│
├── Significant Figures
│   ├── Rules
│   │   ├── Non-zero digits: always significant
│   │   ├── Zeros between non-zero: significant
│   │   ├── Leading zeros: NEVER significant
│   │   └── Trailing zeros after decimal: ALWAYS significant
│   └── Operations
│       ├── Addition/Subtraction: match decimal places
│       └── Multiplication/Division: match sig figs
│
└── Errors
    ├── Types
    │   ├── Systematic — consistent, correctable
    │   └── Random — unpredictable, reducible by averaging
    ├── Measures
    │   ├── Absolute error: |$\Delta A$| (same units)
    │   ├── Relative error: $\Delta A$/A (dimensionless)
    │   └── Percentage error: ($\Delta A$/A) × 100%
    └── Propagation
        ├── Sum/Difference: add absolute errors
        ├── Product/Quotient: add relative errors
        └── Power Aⁿ: multiply relative error by n