Question

What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the units of the first rate are both/all distinct from that of the converted rate, but it still represents the same measurement.

Answer 1

We have two rates, A and B.

If we want that the units of A can be converted into the units of B, then we must have that the units of A represent the same measure that the units of B.

What does this mean?

For example, if A is written in distance over time, then B must also must have units of distance over time.

An example would be:

units for distance = meter, kilometer, feet, etc.

units for time = hour, minute, second, etc-

Then we could have:

[A] = [km/h]

[B] = [m/min]

Then the units of A could be converted into the ones of B, because both of them have the same physical meaning.

Concluding, you only can convert units that represent the same physical quantity, for example, if you have one quantity in meters, for example:

10m

You only can convert this to other units of distance, remember to do the correct conversion, if we would want to write this in cm, you should remember that:

1m = 100cm

Then, 10 times one meter is 10 times 100 cm

10m = 10*(1m) = 10*(100cm) = 1000cm