Unit conversion

Convert 1 erg into joule using dimensional analysis

1 erg = 10⁻⁷ joule. Energy is [M L² T⁻²], so only the powers of mass, length and time decide the factor.

Mass×10^-31 g = 0.001 kg

Length²×10^-41 cm = 0.01 m

Time²×1s in both systems

1 erg 10⁻⁷ joule

Working

Step by step

The dimension of energyEnergy has the dimensions [M L² T⁻²]. Only the powers of M, L and T matter for the conversion.
The conversion ruleA quantity with dimensions [M^a L^b T^c] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [L₁/L₂]² [T₁/T₂]⁻².
The size of each base unitM: 1 gram (g) is 0.001 kilogram (kg). L: 1 centimetre (cm) is 0.01 metre (m). T: 1 second (s) is the same in both systems.
Put the numbers inn₂ = 1 [1 g / 1 kg] [1 cm / 1 m]² [1 s / 1 s]⁻²
Work out each bracket[M₁/M₂] = 0.001; [L₁/L₂]² = 0.01² = 10⁻⁴; [T₁/T₂]⁻² = 1⁻² = 1
Multiplyn₂ = 1 × 0.001 × 10⁻⁴ × 1 = 10⁻⁷
The answer1 erg = 10⁻⁷ joule

Questions

How do you convert erg to joule?

Energy is [M L² T⁻²]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 1 erg = 10⁻⁷ joule.

What is 1 erg in joule?

1 erg = 10⁻⁷ joule.