How many ergs are there in 1 joule?

Concept: The SI unit of energy is the joule (J), defined via its base units as 1 J = 1 kg·m2/s2. The CGS unit of energy is the erg, defined as 1 erg = 1 g·cm2/s2. Converting a derived unit such as energy between the SI and CGS systems means substituting the base-unit conversion factors for mass and length into this dimensional formula.

1. Write the base-unit conversions needed: 1 kg = 103 g and 1 m = 102 cm.

2. Substitute both into the definition of the joule: 1 J = 1 kg·m2/s2 = (103 g) × (102 cm)2/s2.

3. Expand the squared length term first: (102 cm)2 = 104 cm2.

4. Multiply the powers of ten: 103 × 104 = 107, so 1 J = 107 g·cm2/s2 = 107 erg.

Cross-check: This matches the standard SI-to-CGS conversion factor for energy — multiplying an energy value in joules by 107 gives the equivalent value in ergs — independently confirming the derivation above.