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You do not want to change the dimension, just how you express the quantity of the dimension (in different units). Therefore, the conversion factor must be dimensionless. So if your dimension is time, for example. A certain amount of time has passed, say 300 seconds. The amount of time is the same, regardless of what units you express it in. 60 seconds = 1 minute. Divide both sides of this 'equation' by (60 seconds) and you have: 1 = (1 minute)/(60 seconds). So if you multiply 300 seconds by [(1 minute)/(60 seconds)], it is the same as multiplying by 1, which is dimensionless. In this example: (300 seconds)*(1 minute)/(60 seconds) = 5 minutes. So, 300 seconds is the same as 5 minutes, and both are expressions of the same amount of time.

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Q: What does a conversion factor need to equal in the dimensional factor?
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