Foundation · Explanatory preview
Powers of ten and physical units
Powers of ten shift the decimal place. A physical quantity is a number multiplied by its unit; dropping the unit destroys its physical meaning.
Original explanatory text; editorial review pending. This is not a translated source passage.
How do we write very large or very small physical measurements compactly?
Microscopic measurements in physics involve scales far outside everyday experience. Writing numbers as a coefficient between 1 and 10 multiplied by a power of ten keeps significant digits clear and avoids counting long strings of zeros.
Units attach physical dimensions to numbers. A distance of 1 micrometre (10⁻⁶ m) squared is 10⁻¹² m², not 10⁻⁶ m². Calculations must keep units alongside numbers through every algebraic step.
One worked example
- 1 micrometre (1 μm) equals 10⁻⁶ metres (0.000001 m).
- A typical Brownian displacement of 6 μm after one minute is 6 × 10⁻⁶ m.
- Squaring this displacement gives (6 × 10⁻⁶ m)² = 36 × 10⁻¹² m² = 3.6 × 10⁻¹¹ m².
A stopping point: Every physical number must carry its units, and powers of ten apply to both coefficient and unit.
Read as Markdown · All foundations · Return to the Brownian argument
Your browser’s Back button returns to the passage that brought you here.