Expert: Josh - 5/5/2005

Question
How are a centimeter, a ilogram and a milliliter the same? How are they diffrent? Explain.
I am having a really hard time on this one.  

Answer
Hi Jasmine,

I'm kind of with you on this one. This question is badly phrased. The only thing in common that I can see, is that we are referring to one unit of something.

While these units of measurement refer to different physical attributes, (centimeter relates to length or distance, kilogram relates to weight and millilitre relates to volume), their meaning are lost when translated into a mathematical expression, which is dimensionless.

All these things are expressed as 1.
One unit with respect to a centimeter.
One unit with respect to a kilogram.
One lot of one millilitre.
They are scalar values, simply written as 1.

The person doing the maths has to know what they are dealing with. Whether this one unit of measurment measures length, weight or volume.