Converting area and volume units
A length conversion factor is applied once for every dimension, so it appears twice for area and three times for volume. That is why 1 m² equals 10 000 cm², and 1 m³ equals 1 000 000 cm³.
A worked example
Suppose you need to change 45 000 cm² into square metres. Since 1 m is 100 cm, a square metre measures 100 cm × 100 cm, which is 10 000 cm², so dividing gives 45 000 ÷ 10 000 = 4.5 m². Now suppose you need to change 2.5 m³ into cubic centimetres. A cubic metre measures 100 × 100 × 100 = 1 000 000 cm³, so multiplying gives 2.5 × 1 000 000 = 2 500 000 cm³. Recap: square the length factor for area, and cube it for volume.
The mistake people actually make
The most common mistake is dividing 45 000 cm² by 100 and reporting 450 m². That calculation converts only one dimension of the square, but the square extends 100 cm horizontally and 100 cm vertically, so both dimensions need converting.