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Questions tagged [unit-of-measure]

For questions related to conversion of units.

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Quesiton about finding bulk and particle density

The mass of the moist soil = 8126 g; the mass of the dry soil = 7239 g; the volume of the water needed to fill the hole = 3810 cm3. What is the total porosity (%) of their soil? The hole is about 10cm ...
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1answer
27 views

weight of ideal soil (given 2 different densities)

QUESTION - What is the total weight, in pounds, of $1$ cubic meter of an ideal soil including the soil solution. You can assume that the particle density of the soil solids = $2.65$ Mg/cubic meter and ...
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14answers
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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 ...
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1answer
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How to convert $\ kWh/m^2 $ to $\ Joule/kg$

How to convert $$\ kWh/m^2$$ to $$\ Joule/kg$$ I want to compare the radiation produced by the sun over a location (where I live in, measured in $\ kWh/m^2$), to the radiation a person gets from a ...
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0answers
38 views

Why do not we use radian unit sign well? [duplicate]

Mentioned the word) Radian-unit-sign, rad, unit, radian, pure number, ratio, symbol, speed, distance, time
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2answers
38 views

Difference between Celsius and Fahrenheit leads to unexpected observations.

Say city A has a temperature of 54 F(12.2 C) and city B has a temperature of 44 F(6.7 C). Their difference is 10 F which is about -12.2 C. I mean what!? This means that 44 F(6.7 C) > 54 F(12.2 C) or ...
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0answers
28 views

Are percentages scalable?

I have data made up of percentages but no idea how they were calculated. I am using this data to demonstrate Benford’s Law and so far it does follow this law! But one of the properties of sets that ...
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3answers
81 views

What is a valid unit of measurement?

Ok, so this is a bit of an odd question. It is sort of a physics question, but I felt it was more appropriate here. Feel free to suggest another venue. Let's just look at a simple example. We'll use ...
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1answer
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Medical Units into grams

I'm trying to figure out how to divide a medicine up by millions of units into grams or half grams and figure a group like this who play with various math problems might be able to help: What I know ...
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0answers
24 views

Mixing two different essential oils to their maximum safe dilutions in one carrier oil

I want to mix cinnamon bark essential oil (safe at a maximum 0.5% dilution) with tea tree essential oil (safe at a maximum 15% dilution) in shea butter. Shea butter is safe undiluted. The above ...
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0answers
20 views

Conversion from drops to mgs

If the bottle has 500mgs in it and 20 drops equals to 6ml. How many drops do I need to order to get 350 mgs?
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4answers
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Why km$^2$ and not (km)$^2$?

Why don't km$^2$, cm$^3\ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.
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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. $$T(t)=T - (1 - e^{-kt})(1 - B - L^2)$$
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1answer
13 views

Air pollution and measurements: deciliter vs cubic meters

If a deciliter of air has 5000 micrograms, how much would be in a cubic meter? (Particulate matter smaller than 2.5 microns is measured in decileters, larger than 2.5 are generally measured in cubic ...
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3answers
196 views

How much longer does it take to paint a similar box with $5$ times more volume?

This is a question from a precalculus class that I'm a TA for. You build a box that has a volume of 100 cubic feet. It takes two people ten minutes to spray paint this box. How many minutes does it ...
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2answers
92 views

Why is the area of a rectangle with sides a and b defined as axb?

Imagine $a \times b$ was not defined and we need to come up with something. Here is the justification I could come up with: Suppose, I have to measure this thing called area, I have to come with a ...
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1answer
38 views

What are the units of the gravitational constant of the universe $G$?

This is a homework question from a precalculus class that I'm a TA for. The force $F$ between two bodies of mass $m_1$ kilograms and $m_2$ kilograms whose centers of mass are a distance $r$ ...
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1answer
32 views

Explain units for negative exponent

From a textbook of recent publication; "The average radiation on the Earth’s surface is $340 W m^{−2}$." I get the 340W. I presume m is meters. How does a minus 2 affect a meter, rather a square ...
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3answers
56 views

Is 0.1 km equals to 100.0 m (in context to significant figures)?

The number of significant digits in 0.1km is 1 and we know that 1 km = 1000m. This then implies that the 0.1 km is equal to 100.0 m, but the rule says the change in units doesn't affect the number of ...
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2answers
20 views

How do significant figures work in a cross unit division?

In one of my problems, I needed to find a slope on a graph with different units in physics. 309 cm² - 0.0 cm² / 100 cm - 0.0 cm The answer is A = 3.09 r² with A being area and r² being radius ...
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0answers
19 views

Quadratic relationship between units?

Most units I can think of in a given quantity is defined with a linear relationship between them. Is this true for all units? I'm thinking of generalizing conversion factors on this formula: y = x * ...
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Units within a log after integration [duplicate]

Let $x(t)$ and $a$ be in unit meters, and $t$ unit time. If we look at the indefinite integral $$ \int\frac{\frac{dx}{dt}}{x(t) + a} dx $$ then we note that the units of the above expression are $\...
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2answers
42 views

Wich number is the dividend and which is the divisor when it comes to finding unit prices [closed]

How do I know which number to divide by when I have the following question: A runner completes a 10 km race in 0.75 hours. How long will it him take to complete 42 km? So I have to divide 10 and 0.75 ...
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0answers
44 views

Using a continuous failure probability to get reliability $R(T) = \exp(-\int_{t=0}^T h(t) dt)$

I have a continuous process for which I want to compute the probability that it did not fail until time $T$. I tried the reliability / survival function: $$ \begin{align} R(T) = \exp(-\int_{t=0}^T ...
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1answer
42 views

Numerical equality symbol for variables with different units

Good day! I wonder, is there any equality symbol for variables with different units of measurements? For instance, it is given $Ce = 3$ $[V*s/rad]$ which is back-EMF constant of a motor and $Cm$ - ...
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1answer
18 views

What is the difference between Algebra Ratio and Unit Conversion

My apologies for the dumb question. I was wrapping my head around this question - listed below. I’m a bit confused as to why when we have 2C equal 3D units and are trying to convert from a D unit to a ...
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1answer
51 views

Simple differential equations (confusion over the “rate” of change)

Consider the following very simple scenario. Suppose that, after $t$ hours, the number of people at a small theme park is $p$. $p$ and $t$ are continuous variables. On average in each hour, $0.5p$ ...
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2answers
61 views

Changing Units to Solve Differential Equation

If this should be on SE Physics instead, let me know, and I'll post there instead. I have a diff eq. of the form $\ddot x + \beta \dot x^2 = 0$ Maybe there is a simple analytic solution, but I haven'...
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1answer
78 views

Does the dot notation above a variable not always mean a derivative?

I came across the equation: $\frac {\partial v} {\partial t}= g \dot v - \frac {v^2} r$ Where $v$ is a velocity in $\frac m s$, $r$ has units of $m$, and $g$ is gravity (units of $\frac m {s^2}$). ...
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1answer
51 views

How do I change millimeters into degrees? [closed]

I have a Flange gasket with a pcd of $833 \ \text{mm}$ and I need to put a slotted hole at $12$ equal places that is $18 \ \text{mm}\times 28 \ \text{mm}$ long with rounded ends. How do I divide the $...
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1answer
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Understanding the units of the equations [closed]

I am reading a paper and there are some equations whose units I do not understand and hope some one can help. The paper is this for the reference (all the equations are in page 2): https://www....
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5answers
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Conversion of $2\:\text{m}^2$ in $\text{cm}^2$

I had an evaluation and had to go from $2\:\text{m}^2$ to $\text{cm}^2$ and I made a rule of three simple: $1\:\text{m}^2 = 10000\:\text{cm}^2,$ $2\:\text{m}^2 = 20000\:\text{cm}^2.$ But the teacher ...
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0answers
23 views

How to calculate speed from time and distance…

I understand the formula for calculating speed. However, I'm not very good at the conversions. I'm trying to figure out the speed of a baseball pitch, based on the distance and time. A ball pitched ...
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4answers
1k views

What are the units of the $\sin(10^\circ)$? [closed]

Say I measure the angle of incidence to be $10^\circ$, what is the unit for $\sin(10^\circ)$?
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3answers
41 views

Parentheses around Whole Expression vs Leaving out Exponents

What is the difference between: 5 cm^3 and (5 cm)^3 Is there any difference in the sum of this equation? If not, can ...
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1answer
83 views

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 ...
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0answers
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A very bizarre confusion

This is a maths problem I am not sure, but I know that normal paper money is approximately $1\text{mm}$ thick. But why is there $100$ notes in a $1\text{cm}$ thick paper money stacked in say banks? ...
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0answers
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How to represent sets of quantities with different units mathematically?

Let's say I have two nonnegative rational quantities – e.g., time and potatoes – that I want to represent by (potentially infinite) sets of elements $T$ and $P$. What would be a correct mathematical (...
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1answer
25 views

Express $1$ Quad/yr in units of kW*hr/day/person [closed]

For calculating the -per person- part, we are going to be using the population of the USA, i.e, $3\times10^8$.
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2answers
2k views

log(A/B) = log(A)-log(B), where A and B have units [closed]

We all know that $$\log\left(\frac{A}{B}\right) = \log(A)-\log(B)$$ However, in the case where $A$ and $B$ have (identical) units, such as kilograms, the right-hand side cannot be performed because ...
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1answer
128 views

I do not know how to convert a feet decimal

I have a height of 6.075 but need to convert in to normal form(1'5"). how do i do this.I have a math fair project coming up and have no clue how to change this.
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0answers
53 views

$10^{20}$ eV to ton of TNT with the correct number of significant figures

I am trying to convert $10^{20}$ electron-volt to ton of TNT. What I know is: There are $10^{20}$ eVs which is 1 sig fig. 1 electron-volt = $1.602*10^{-19}$ J which is 4 sig figs. 1 ton of TNT = $...
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0answers
18 views

Finding the unit

I have the equation: And the following units: for time is the day for the alfa and ...
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1answer
32 views

Is this conversion correct? Liters per 100 Km at given speed (km/h) to mililiters per minute

For example 8L/100km @ 80km/h First thing I did was get the time I would take to complete 100km with my current speed $$ \frac {100 \text{ km}}{80\text{ km}/\text{h}} = 1.25\text{ h}$$ then $$=\...
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3answers
2k views

Why are radians dimensionless? [duplicate]

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 ...
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0answers
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What are formally measurement units?

I was wondering about how to define formally in mathematics the use of units of measure. Initially I was thinking about taking the algebra of rational functions over the indeterminates which are ...
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1answer
60 views

Cancelling units of empirical equation

OK this is probably a simple question, but I can't seem to find a good answer. I know that in dimensional analysis the units on both sides of the equation must be equivalent; I suppose the simplest ...
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1answer
19 views

polynomials with numbers and matrices entries

I found somewhere in a book, that it is defined the polynomial $p\in\mathbb C[X]$ with k degree and then they write down the polynomial for 2 values: $A\in M_n$ and $a\in\mathbb C$, like this: $p(A)...
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1answer
54 views

Where can I find info on algebra with units of measurement?

If you add two magnitudes with same units you get an answer which is in the same units, but adding different units "does not make sense". But this is not true with multiplication, because you can ...
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0answers
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A paradox regarding a being able to measure a distance between two points with an infitely accurate distance unit

This question is related with the Cardinality of the continuum and Zeno's paradox about Achilles and the tortoise regarding the concept of infinity. I would like to know if the following guessings are ...