# Unit conversion help

Hello,
I need to convert a moment of intertia value given in g*cm^2 to kg*m^2, and was hoping someone could give me a run down of the method behind these kind of conversions. Do I simply assume that since g to kg is a factor 0.001 and cm to m is 0.01, that I can apply a factor of 0.00001 to my initial value? I feel that that method would be fine for say, g*cm to kg*cm, but I'm not sure how to account for the squared dimension. Any help/explanation would be appreciated. Thanks.

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Integral
Staff Emeritus
Gold Member
In general when converting units set your quantity to be converted and your conversion factor up as a multiplication of fractions. For example from m/s to cm/s
$$10 \frac m s * 100 \frac {cm} {m} = 10*100 \frac m s * \frac {cm} {m} = 1000 \frac {cm} s$$
Note that in this example the m in the numerator cancels the m in the denominator, leaving only cm in the numerator.

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okay, i see what you mean, i've used that technique before, but the confusion came from two places for me.
1) that i'm dealing with a squared quantity, so would the conversion be 1000cm^2/m^2?
2) that the it's g*cm^2, rather than g/cm^2, leaving me wondering how to actually set up the calculation.

i'm sure it's quite obvious how to do this, but the way i set it up, the units don't cancel out. i need to be certain of this conversion before i can begin to do the problem, since it's for an online assignment for which i have only one attempt. could you possibly lay out how you'd set it up for the case of my calculation? i know it's not usually acceptable to 'give' the solution away in this forum, but the physics of the problem are not a concern, just this one calculation. okay, thanks again for your help.

Integral
Staff Emeritus
Gold Member
The method is the same just square the conversion factors. So

$$10m^2 = 10 m^2 * (100 \frac {cm} m)^2 = 10 * 10^4 m^2 \frac {cm^2} {m^2} = 10^5 cm^2$$
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