Units, Measurement Systems and Percentage/Proportion in Workshop Contexts
Units questions check that you can convert cleanly, use SI prefixes and apply percentage or proportion to tolerances and mixtures.
SI and conversions
Base units are metre, kilogram, second, ampere, kelvin, mole and candela. Derived units include N = kg·m/s², Pa = N/m², J = N·m and W = J/s. Prefixes: kilo 10³, milli 10⁻³, micro 10⁻⁶.
- 1 inch = 25.4 mm exactly; 1 ft = 304.8 mm; 1 lb = 0.4536 kg; 1 kgf = 9.807 N; 1 hp = 746 W; 1 bar = 100 kPa.
Percentage and proportion
Percentage error = |measured − true| ÷ true × 100. Percentage change uses the original value as denominator. For mixtures, parts by mass sum to the total: mass of component = percentage × total mass.
Worked example
A 3/8 inch dimension is 0.375 × 25.4 = 9.525 mm. A part is measured at 9.48 mm. Error = 9.525 − 9.48 = 0.045 mm; percentage error = 0.045 ÷ 9.525 × 100 = 0.47%. For a bronze of 90% Cu and 10% Sn by mass, a 25 kg melt needs 22.5 kg copper and 2.5 kg tin.
Traps
- Using the new value as the denominator in percentage change.
- Cancelling units incorrectly, such as mixing N and kgf.
- Rounding 25.4 to 25 and losing accuracy.
- Confusing percentage points with percentage change.
- Applying a tolerance percentage to the tolerance instead of to the nominal size.