What is the difference between a physical quantity and a number?

Question

Accepted Answer

Welcome back everyone. How is a physical quantity different from a number? We have four different answer choices A through D which differ in the descriptions or definitions for these two terms. Let's begin by differentiating via notes, our understanding of a physical quantity versus a number beginning with the more simpler one which is a number, we can recall that a number is simply just an integer or numerical value. And this numerical value does not have units of measurements. So for example, we can have an integer such as 3.7 times 10 to the negative third power, which is simply just going to represent a value that we have no association to describe something without giving it a unit. And so because this is a unit less integer, this is simply just a numerical value. On the other hand, for a physical quantity, we're going to recall that a physical quantity is measurable for a physical property. So an example would be something like the acidity or basic of a solution, which is a physical property. Now, the physical quantity that would define that would be the concentration of hydrogen ions or protons in solution. And this would also be associated with the ph of that solution, which is ultimately a dimensionless, a dimensionless physical quantity. However, to be even more clear, we can think of a physical quantity with dimensions, which would be something like 3 mL or three liters or three cubic centimeters, which all are physical quantities for the physical property of volume where we're called that volume defines the amount of space a substance takes up. And so ultimately, we can also include the note that for a physical quantity, we should have a numerical value with a unit of measurement to define that value. So based on what we've outlined, going back to our answer choices A through D looking at choice A, it states that a physical quantity is a numerical value with a unit of measurement which we can agree with. Whereas a number is simply a value without a unit of measurement. And these two statements exactly align with what we noted below. So we would say that choice A looks like a correct choice. But let's keep considering our other options such as choice B where it says that a physical quantity is a numerical description with a unit of measurement. And a number is simply a description without a unit of measurement. So because for the first part, physical quantity, it states that it is a numerical description, we want to keep using the word value. So we would not agree with the first part of part B and we also would not agree with part B stating that a number is a description, again, a number is a value and a physical quantity is a value. But the difference is that a physical quantity has the addition of a unit of measurement. So choice B is incorrect for those reasons. And then we have choice C which again states that a physical quantity is a numerical description. So that is also again incorrect. We needed to state that a physical quantity is a numerical value with a unit of measurement. Then in choice D it states that a number is a description without a unit of measurement. And we would not agree with that because we need to say that a number is still a value. So choice D is also incorrect. And that leaves us with choice A which correctly defines how a physical quantity is different from a number stating that a physical quantity is a numerical value with a unit of measurement. Whereas a number is simply a value without a unit of measurement. So a is our final answer. I hope that this made sense and let us know if you have any questions.

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What is the difference between a physical quantity and a number?

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