There was the following question on a practice exam: Question 2: True or false?

Question

There was the following question on a practice exam:

Question 2:
True or false?
A scalar quantity only has a magnitude. It does not have a direction associated with the number.

Now to me this seems to be true because a scalar only has a magnitude and no direction. However, the answer key says this question is false with the following reason:

1.
False
Reason: This answer is correct because a scalar quantity has no direction, however, it has a number and a unit (e.g. 12 kg).

Isn't this answer being extremely picky? Does a scalar always have to have units? Is this answer an error?

Explanation / Answer

I would agree that it was not worded the greatest. Scalars do not always have to have units though. This is because they are used to describe one dimensional quantities, that is, quantities which require only one number to completely describe them. Some scalars are time, temperature, location along a line, volume, speed, mass, etc. Just, things that you can manipulate (Like if I added 20 grams of flour to a cake mix that already had 5 grams, meaning the new value would be 25 grams).Which I'm sure you already know. Some scalars do not have units though. The simplest Scalar would be just a single unitless number, which may take any value. A more complicated Scalar might be one which is bounded above and below. Making it more complex, the Scalar MAY have units, and it may have auxiliary properties which describe the environment in which the primary Scalar number/units is applicable. So seconds for time, meters^3 for volume, etc. The question was just worded poorly. The majority of the time the scalars people need for classes are all with units so the book probably just went off of that.

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