How to Convert Units

The idea: multiply by a fraction equal to 1

Since 1 in = 2.54 cm, the fraction (2.54 cm ÷ 1 in) equals 1. Multiplying any length by it changes the units but not the length itself. Choose the fraction so the unit you want to get rid of cancels:

This is called the factor-label method or dimensional analysis. The units tell you whether you have set the fraction up correctly: if they do not cancel, flip it.

Multiply or divide?

Converting to a smaller unit gives a bigger number (multiply): 3 m = 300 cm. Converting to a larger unit gives a smaller number (divide): 300 cm = 3 m. A quick sanity check catches most mistakes.

Multi-step conversions

Chain factors when there is no direct one:

Squared and cubed units

For area, apply the length factor twice; for volume, three times.

This is the most common unit-conversion error: 1 m² is not 100 cm².

Rates

Convert the top and bottom separately:

Temperature is the exception

Celsius and Fahrenheit have different zero points, so you cannot just multiply. Use °F = °C × 9/5 + 32. But a temperature difference converts with the factor alone: a rise of 10 °C is a rise of 18 °F.

Precision

• Many factors are exact by definition (2.54, 0.3048, 0.45359237, 3.785411784) — rounding happens only at the end.
• Keep a few more digits in intermediate steps than you need in the answer.
• Round the final result to match the precision of your original measurement.