Convert quantities without changing what they measure

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Convert quantities without changing what they measure

A conversion changes the numerical description of a quantity, not the physical quantity itself. If one metre is 100 centimetres, a length in metres is multiplied by 100 to express the same length in centimetres. Decide whether the new unit is smaller or larger before choosing multiplication or division.

Area and volume conversions use squared and cubed factors. One square metre contains 100 × 100 square centimetres, so 1 m² = 10 000 cm². One cubic metre contains 100³ cubic centimetres. Applying the length factor alone produces an incorrect area or volume.

Compound units require all relevant conversions. For speed, 1 m/s corresponds to 3600 metres per hour, or 3.6 km/h. The same conversion reasoning applies to algebraic quantities: a length of x metres is 100x centimetres.

Worked example: Convert 2.5 m² into cm².

The length conversion factor is 100.

Square that factor for area.

Multiply 2.5 by 10 000.

Answer: 25 000 cm².

Check your understanding: How many cubic centimetres are in 1 m³?

Answer: 1 000 000.

Why: There are 100 centimetres along each of three dimensions.