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.

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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…
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Is there a basic "unit" of measurement in math

I am wondering if there is a basic unit in math. $$3\ cm \times 2\ cm = 6\ cm^2$$ The $cm$ is a unit of measurement, but what about: $$3\ cm \times 2 = 6\ cm$$ Should the $2$ have a unit of counting? Like I have $2$ (amount of stuff) $3\ cm$…
Madfrog
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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
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What *is* 1 cm$ ^{ -3}$?

I am having trouble with notations like 1 cm$^{-3}$, especially since I am converting them between compound units. Is there a way to express 1 cmcm$^{-3}$ without writing the negative exponent? The particular queston I was asked was: The EC…
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Square Inches vs Inches Squared

I was just asked the question, is there a difference between 12 square inches and 12 inches squared. At first I assumed that 12 inches squared mean a square with sides of 12 inches. In this case the answer would be no. 12 inches squared would be 144…
Jordan
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Division of Compound Units

Why are compound units of speed,density etc. expressed in terms of a numerator and a denominator? For example, m/s, kg/m3 etc. I've always understood division as either the inverse of multiplication, splitting a collection of objects into n equal…
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How would you interpret this unit conversion question?

The following question is copied word for word from my textbook, which is what causes me to be so confused about the contradiction that it implies. The question: For gases under certain conditions, there is a relationship between the pressure of…
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convert unit of measure mpg->lp100km

So, I have the problem to convert mpg to lp100km. I have tried to calculate them by hand, given that 1 mile = 1.60934 km and 1 gallon = 3.78541 litres, and it yields me like: 1 mpg = 235.133 lp100km However, when I searched for the conversion…
Aaron
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Conversion Question

A heavy rain fell on a city for 26 minutes, at a rate of 3.9mm/hr. If the area of the city is 244km^2, how many gallons of water fell on the city that day?
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How do I convert 60mph to light years per second using scientific notation?

I tried to follow along with this units video (https://youtu.be/hQpQ0hxVNTg) and convert 60 miles per hour to light years per second. I don't get the same answer as the video does. I feel really dumb! I just try to multiply through? and…
lonious
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Formula conversion with units

I'm working with the following equation: $$MU=1000\gamma k [ONPG] \delta \frac{1}{V} \frac{N_z}{N_{cells}}$$ To which I would am trying to get to the following: $$MU \times mL \times min \times 0.5=\frac{N_z}{N_{cells}}$$ The paper this is based off…
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If angles are unitless, what are radians and degrees?

In $s=r\theta$, is $\theta$ unitless? Isn't it measured in radians? If angles are unitless, what are radians and degrees? Please clarify.
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Determine measure unit.

Determine a measuring unit of $B$ and $k$ if $T$ is a temperature in Kelvins, $t$ is time in seconds and $L$ is the length in meters. $$T(t)=T - (1 - e^{-kt})(1 - B - L^2)$$
Lind
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convert joules to watts

I am investigating the changes in heat fluxes from a given body of water where the measurements are shown in units of W/m2. There are alternative methods for determining the heat fluxes from a given body of water by calculating the change in…
KatyB
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Scaling and zooming the Mandelbrot Set

Whenever I would see Mandelbrot zoom videos pop up on my YouTube, I would always watch the entire thing. It always amazed me. Recently I thought how "much" are we zooming in. How small of a point in the complex plain are we going. Each video gives a…
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