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I would like to know the general method of converting between units. For example converting Joules to $\frac{g\cdot cm^2}{s^2}$

I assume it's possible because the SI unit of energy is $\frac{kg\cdot cm^2}{s^2}$ so is it as simple as going from J to $\frac{kg\cdot cm^2}{s^2}$ and then times 1000 to get $\frac{g\cdot cm^2}{s^2}$?

If so then how does one know how many J in 1 $\frac{kg\cdot cm^2}{s^2}$? Is it something you have to learn like 1kg is 1000g?

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    $\begingroup$ Your unit is wrong. The SI unit of energy is the Joule, which is $\frac{kg\cdot m^2}{s^2}$ $\endgroup$
    – mmesser314
    Commented Nov 14, 2020 at 19:47

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$1J=1kg.m^2/s^2$.

To convert this to $erg=g.cm^2/s^2$ replace $kg$ by $10^3 g$ and $m$ by $10^2 cm$ : $$1J=1(10^3 g)(10^2 cm)^2/s^2 = 10^7 g.cm^2/s^2=10^7 erg$$

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