### Units

1. The fundamental mechanical units (Systeme Internationale) are meters (m), seconds (s) and kilograms (kg).
2. Every equation or sum must have the same units in every term.
3. Arguments of trigonometric, logarithmic or exponential functions must be unitless.
4. Unit conversion is accomplished using conversion factors of the form a / b, where b has the "old" units and a has the "new" ones:
(2 furlongs / fortnight) * (1/8 mile / furlong) * (5280 feet / mile) *
(12 inches / foot) * (2.54 cm / inch) * (1 m / 100 cm) *
(1 fortnight / 14 days) * (1 day / 24 hours) * (1 hour / 60 minutes) * (1 minute / 60 seconds)
= (2 * 1/8 * 5280 * 12 * 2.54 / 100 / 14 / 24 / 60 / 60) m/s

= 0.0003326 m/s ≈ 1/3 mm/s

Note that when converting surface areas or volumes, the conversion factor must be inside the exponent:
2 liters * (1000 cm3 / liter) * (1 m / 100 cm)3
= 0.002 m3
5. Know the following metric prefixes:
• f (femto) = 10-15
• p (pico) = 10-12
• n (nano) = 10-9
• μ (micro) = 10-6
• m (milli) = 10-3
• c (centi) = 10-2
• k (kilo) = 103
• M (Mega) = 106
• G (Giga) = 109
• T (Tera) = 1012
• P (Peta) = 1015

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©2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.