Questions tagged [unit-of-measure]

This tag is meant for questions concerning the use of units in the measurement of a quantity.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement.

For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length.

For most quantities, a unit is necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.

But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the base units and the other units are derived units.

Thus base units are the units of the quantities that are independent of other quantities and they are the units of length, mass, time, electric current, temperature, luminous intensity and the amount of substance. Derived units are the units of the quantities that are derived from the base quantities and some of the derived units are the units of speed, work, acceleration, energy, pressure, etc.

Different systems of units are based on different choices of a set of related units including fundamental and derived units.

290 questions
61
votes
15 answers

Is the percentage symbol a constant?

Isn't the percentage symbol actually just a constant with the value $0.01$? As in $$ 15\% = 15 \times \% = 15 \times 0.01 = 0.15. $$ Isn't every unit actually just a constant? But why do we treat them in such a special way then?
53
votes
12 answers

Why do we require radians in calculus?

I think this is just something I've grown used to but can't remember any proof. When differentiating and integrating with trigonometric functions, we require angles to be taken in radians. Why does it work then and only then?
45
votes
3 answers

Units of a log of a physical quantity

So I have never actually found a good answer or even a good resource which discusses this so I appeal to experts here at stack exchange because this problem came up again today. What happens to the units of a physical quantity after I take its…
Fixed Point
  • 8,109
  • 3
  • 33
  • 49
33
votes
6 answers

Why radian is dimensionless?

Can't understand why we say that radians are dimensionless. Actually, I understand why this is happening: theta = arc len / r Meters/meters are gone and we got this dimensionless. But also we know that angle 57.3 degrees = 1 rad. So, can we use it…
17
votes
4 answers

My teacher said that $2\pi$ radians is not exactly $360^{\circ}$?

A few days ago, my math teacher (I hold him in high faith) said that $2\pi$ radians is not exactly $360^{\circ}$. His reasoning is the following. $\pi$ is irrational (and transcendental). $360$ is a whole number. Since no multiple of $\pi$ can…
Jack Pan
  • 1,714
17
votes
5 answers

How would multiplying money work?

This is a very silly question since nobody will actually do this because it makes very little sense in the real world but I just want to know how would it actually work if possible. For example let us take an amount of 2 dollars and 2 cents and…
15
votes
2 answers

Which distances can I run on my treadmill?

This is a real-world question, prompted by some unusual features on my treadmill and which I thus think about while running. In a sub-menu on my treadmill, I can select a distance that I want to run. If my unit setting is "miles", the distances…
14
votes
2 answers

What is significance of (.) in significant figures?

I read in my textbook (NCERT class 11 chemistry) that 100 has 1 significant figure 100.0 has 4 significant figures 100. has 3 significant figures Including the dot increases the number of significant figures. So what is the significance of this…
Pole_Star
  • 1,122
11
votes
3 answers

Why are radians dimensionless?

According to https://en.wikipedia.org/wiki/Dimensionless_quantity, "A dimensionless quantity is a quantity to which no physical dimension is applicable." The article then explains, a few sentences later, that time, as an example, is a quantity with…
10
votes
7 answers

Difference between units and dimensions

Though this question may seem related to Physics, I think that at the very root this is a mathematical question and so I have posted this on math.stackexchange. Background: Initially I thought that the terms-unit and dimension, refer to the same…
MrAP
  • 3,113
9
votes
5 answers

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the degree into arcminutes and arcseconds, so that "180…
9
votes
3 answers

Arbitrarily discarding/cancelling Radians units when plugging angular speed into linear speed formula?

Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit. For all other cases, you need to introduce the unit conversion fraction, and cancel explicitly. Is it because radians and angles have no relevance to linear…
JackOfAll
  • 4,871
8
votes
2 answers

Why is it valid to treat units as variables?

I've always taken for granted the fact that units can be treated as variables in mathematical expressions. If you have an object that travels $10m$ in $2s$, you can simply divide the length by the time and get $5m/s$. This works well and all, but I…
7
votes
4 answers

Formally, why is it meaningful to multiply, but not add, different units?

I know a bit of dimensional analysis from physics. Simple example, if you have $10J\cdot m^{-1} \times x = 20J\cdot kg\cdot m^{-2}$ then you can deduce that $x=2kg\cdot m^{-1}$, the units being determined in the obvious, natural way. You cannot add…
spraff
  • 1,263
  • 11
  • 22
7
votes
1 answer

How to compare units?

Something is confusing me, it's about real world units vs abstract ones and what should be abstract and absolute. Here's my problem: 1 dog + 1 dog = 2 dogs A dog is an abstract unit, all dogs are different, yet this equation still makes sense. You…
seven-dev
  • 193
1
2 3
19 20