# Tagged Questions

For questions related to conversion of units.

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### If I square a measure in radians, is the result measured in steradians?

Originally, SI units included radians and steradians as base units (now they're considered derived). The fact that they bothered to include radians and steradians is confusing to me. I usually think ...
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### In “10 grams of salt”, is the unit “grams”?

The gram is a unit of mass, so "10 grams" has "grams" as the unit. "10 pounds" uses a different unit. So what is the "salt" in "10 grams of salt", if not a unit? In other words, what is the ...
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### I am having trouble with solving measurment word problems

The problem goes as follows A swimming pool is 15 by 30 ft and a consistent 5 ft deep. You are painting he walls and floor of the pool. If a gallon can of paint covers 250 square feet how many ...
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In science I commonly see the notation $m^{3}$ and $m^{-3}$, especially when discussing the amount of molecules in a volume. What is the difference between those two units? For example, does $1.5\... 1answer 14 views ### How to increase volume from cubic centimeter to a meter? I am trying to figure out how to calculate the change in concentration of an object within a volume, when you increase that volume. For example... Let's say we have 5 flies per cubic centimetre of ... 1answer 20 views ### Interpreting the unit of definite integral I'm calculating a definite integral of a function describing a pressure of certain system where time is the independent variable, that is my function is: $$f(t) \;\text{psi},$$ so e.g.$f(0)\;\text{...
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Can't understand why we say that radians are dimensionless. Actually, I understand why this is happening: theta = arc len / r ...
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### 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 ...
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### How to create equation for updating (Packets and Sheets)

I have (n) Packets containing (x) sheets (1 Packet = x Sheet) where (both x and n are integers). Now I want to sale by Packet and By Sheet I created an excel file but I am very confused on how to ...
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### How to Convert Kilometers/Kilogram (km/kg) to Miles/Gallon (MPG)

I need to convert Kilometers per Kilogram to Miles per Gallon in order to calculate the Carbon Footprint of daily work commuters with vehicles using CNG (Nat Gas). In order to do this, I need to be ...
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### 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 ...
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### 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 ...
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### Mpg to l/100km conversion problem?

We have two vehicles A: old truck that does 17 mpg (13.84 l/100km) B: old car that does 47 mpg (5.00 l/100km) We are looking to replace one of these vehicles with a new one (of the same size)...
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### nondimensionalise an equation

The per capita birth rate of a population is given by $r[1-a(N-b)^2]$, r,a,b are positive parameters,, write down a population model equation such of the form $dN/dt=f(N)$ Nondimensionalise the ...
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### How to use the metric conversion

I know how to use the metric conversion (K h d b d m c) when converting length to length for example 1 m squared to cm, etc. But I want to know how to use the metric conversion when converting from ...
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### Unit and dimension of angles

usually in physics (at least in the SI) angles are regarded as dimensionless. Is it possible to give a dimension (and a unit) also to angles and still have a system of units of measure as coherent as ...
3k views

### 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 ...
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### Units for Measuring Rotation of a 3-Sphere in Four Dimensions

In four dimensions, there can be two orthogonal axes of simultaneous rotation (of two planes), right? Does that mean that we can measure such rotations of a 3-sphere in solid angles, much as we ...
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### Local Solid Angle Units

This is a cultural question: Are there any, even moderately or historically used, units that measure solid angles which are not steradians? Basically, is there a unit x such that x:sr::grad:rad?
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### Software for unit aware calculations?

When doing engineering calculations it is great convenience to do have software that keeps track of units. Example when calculate something trivial as stress: $\sigma = \frac FA$ And be able to ...
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### How to convert a derived unit which contains degrees Celsius?

For instance, I have the following problem: convert: $\frac{{m^2}^{\circ}C}{W}$ to $\frac{ ^{\circ} F * ft^{2} * hr}{Btu}$ Take $x \frac{{m^2}^{\circ}C}{W}$ for instance, how would I convert it to ...
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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, ...
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### unitary mehod apply [closed]

যদি প্রতি 10মিনিট 3 বার গোলাবষন করে 6টি কামান 60ঘন্টায কোন দূগ ভাঙতে পারে তবে 5 মিনিটে 2বার গোলা বষণ করে যে সংখ্যাক কামান ঐ দূগকে ভাঙ্গতে Translation:- If 6 cannons by firing 3 times every 10 ...
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### What formula can I use to calculate how much protein per 100 calories a given food has?

I have an Excel spreadsheet of 529 items all with calories, carbs, fats, and protein listed. I'd like to add a grams of protein per 100 calories column but my math ability is embarrassingly non-...
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### How many square millimetres are in 0.000075 square metres?

Doing my head in a bit.. $0.000 075 \times 100$ = in square cm, and times that by $10 =$ square mm but apparently I'm off by a couple of orders of magnitude.
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### Setting Unknowns to 1

Suppose a square formation of troops 50 meters deep is marching with a dog in the middle of its back rank. The dog runs to the front of the formation, turns around instantaneously and runs back to ...
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### Getting the number of significant digits in a multiplication/division.

What is the result of $$\frac{0.002843\cdot 12.80184}{0.00032}$$ with the correct number of significant digits? In the multiplication above, both have $7$ significant digits I think. Therefore ...
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### Get the mass of air given the dimensions of a room.

The density of air is $1.19g/L$. What is the air's mass, in kilograms, in a room that measures $14.5\cdot16.5\cdot8.0$ feet? The room is is $14.5 \cdot 16.5 \cdot 8.0 = 1914$ cubic feet. We should ...
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### Physics/Math conversion

I'm having difficulties solving this conversion. I know what to do at first but the way to set this up is a bit confusing:
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### When should matrices have units of measurement?

As a mathematician I think of matrices as $\mathbb{F}^{m\times n}$, where $\mathbb{F}$ is a field and usually $\mathbb{F} = \mathbb{R}$ or $\mathbb{F} = \mathbb{C}$. Units are not necessary. However, ...
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### Unit of value calculated by using integral

I have a really simple question that is driving me crazy! I have a program which can log power and the result is a log file which contains two arrays, one with time values that show when a power value ...
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### According to Buckingham Theorem the rank of $A$ should be $2$

A physical system is described by a law of the form $f(E,P,A)=0$, where $E,P,A$ represent, respectively, energy, pressure and surface area. Find an equivalent physical law that relates suitable ...
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### 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 ...
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### Units of Measure conversion

I was wondering if i could get some help trying to create a simple math formula. I recently was given an interview to work as a tier1 programmer and was asked to make a program. I made the whole thing ...
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### Conversion/compatibility of compounded physical units

This question is not so much asking about how to do something, but about whether it makes sense. For instance, converting miles per hour to kilometres per hour makes sense, because both terms have ...
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### How to find average walking time per day

I have calculated that the total walking time for a person is 2990702 minutes in 801 days. I want to know his average walking time per day in minutes. I dont know if I need to convert minutes into ...
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### Unit rules and style convention for division

I'm trying to figure out the preferred way to write unit expressions and division is causing me some confusion. I'm aware of the negative exponent notation, but here I'm looking for a solution using ...
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### How to lay out the conversion of £ $(13 + v^{2}/52)$ per hour to £ per mile

"29. The total running cost of a ship per hour is £ (13 + $v^{2}$/52) where $v$ knots is the speed. if £ $C$ is the cost per nautical mile, write down an equation expressing $C$ in terms of $v$..." ...
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### Why is 1 cubic meter 1000 liters?

Can anyone explain why $1\ \mathrm{m}^3$ is $1000$ liters? I just don't get it. 1 cubic meter is $1\times 1\times1$ meter. A cube. It has units $\mathrm{m}^3$. A liter is liquid amount measurement. ...
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### In terms of units: is integration equal to multiplication and differentiation equal to division as a general rule?

The question From practical experience, I know that the unit of an integral - resulting from integration of an expression with respect to a variable with a unit (i.e. non-dimensionless variable) - is ...
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### Unit conversion equation

My company compares office rental price in multiple currency and units. Users can choose to view the price in USD per square foot or EUR per square metre or GBP per square yard, etc. For the sake of ...
4k views

### 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 ...
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### simple weight conversion

I need some help of mathematicians :D , So here is the problem So i am calculating calories in foods. If I google for "calories in banana" , I get this ...
I was writing a unit converter for an industrial setting. To ensure that $\frac 0 0$ and $\infty$ never show up in the user interface I made a rule that no unit conversion factor can ever be zero. ...
How do you take the inner product of a vector whose components have different units? For example, what is the inner product of $\langle1m, 1s\rangle$ and $\langle2m, 3s\rangle$?