For questions related to conversion of units.

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22
votes
9answers
7k views

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 ...
11
votes
5answers
2k 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 ...
7
votes
4answers
245 views

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 ...
6
votes
5answers
736 views

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 ...
5
votes
4answers
16k views

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 ...
5
votes
3answers
1k views

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 ...
3
votes
3answers
137 views

Where should the exponent be written in numbers with units of measurement?

If you are to calculate the hypotenuse of a triangle, the formula is: $h = \sqrt{x^2 + y^2}$ If you don't have any units for the numbers, replacing x and y is pretty straightforward: $h = \sqrt{4^2 ...
3
votes
7answers
200 views

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 ...
3
votes
3answers
295 views

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 ...
3
votes
2answers
2k views

Difference between “sq km” and “km sq”

If I have a square with side $2\ \text{km}$, what is its area: $2\ \text{sq km}$ or $4\ \text{km}^2$?
3
votes
1answer
310 views

Can you calculate an area of a curve using a string?

Take a look at this curve. Imagine that I have drawn this on a paper, and that I want to find the area of it. (The thickness of the line is assumed to be constant). Assume that I use a string to ...
2
votes
2answers
324 views

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 ...
2
votes
1answer
229 views

Radian, an arbitrary unit too?

Why is the radian defined as the angle subtended at the centre of a circle when the arc length equals the radius? Why not the angle subtended when the arc length is twice as long as the radius , or ...
2
votes
2answers
63 views

Can minutes be used to measure the length?

I am using an Old American maths textbook and it uses US customary units. For the length, they use minutes (like $6'$ for the altitude of a triangle). How is this related to foot which is the unit of ...
2
votes
2answers
181 views

Using Ruler to Measure Irrational Number

If I would draw a right triangle with legs of length 1 centimeter with a ruler then its hypotenuse should be equal to $\sqrt2$ which is an irrational number - therefore its decimal representation, ...
2
votes
2answers
24 views

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 ...
2
votes
2answers
97 views

How do you take the inner product of a vector whose components have different units?

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 $\langle2m, 3s\rangle$?
2
votes
1answer
24 views

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 ...
2
votes
1answer
40 views

Is a unit conversion factor ever legitimately zero?

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. ...
2
votes
1answer
32 views

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 ...
2
votes
1answer
34 views

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, ...
1
vote
2answers
128 views

How do I have to interpret $\mathrm{nm}^2$?

My short question: How many $\mathrm{m}^2$ are $\mathrm{nm}^2$? Do I have to interpret it as $\mathrm{nm}^2=(\mathrm{nm})^2=(10^{-9}\mathrm{m})^2=10^{-18}\mathrm{m}^2$ or shall it be ...
1
vote
2answers
196 views

Is there a limit to how exact $\pi$ can be calculated? [duplicate]

Possible Duplicate: Do We Need the Digits of $\pi$? Working out digits of Pi. What are the limitations? Faster computers More accurate measuring devices
1
vote
2answers
144 views

Square Root Yields Different Result After Unit Conversion [duplicate]

This is boggling my mind. The square root of 100 seconds is 10 seconds The square root of ...
1
vote
2answers
116 views

How can I convert between powers for different number bases?

I am writing a program to convert between megabits per second and mebibits per second; A user would enter 1 Mebibits p/s and get 1.05 Megabits p/s as the output. These are two units of computer data ...
1
vote
1answer
2k views

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 ...
1
vote
2answers
98 views

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 ...
1
vote
2answers
23 views

What is the length of the bar needed to represent 75 kilometers( in centimeters)?

In a bar graph, 1 centimeter represents 30 kilometers. What is the length of the bar needed to represent 75 kilometers( in centimeters)?
1
vote
1answer
38 views

problem with units when calculating with angles

I have this formula to calculate the refraction of a star in the sky (the difference between where the star appears and where it really is.) $z_0 = z + 60''\times \tan z$ where $z_0$ is the ...
1
vote
1answer
17 views

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 ...
1
vote
3answers
53 views

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, ...
1
vote
1answer
60 views

Taylor's series and the function argument dimension

I've stumbled over an interesting question. In $\cos(x)$, $x$ is measured in, say, radians. When I expand cosine in Taylor's series, I have the terms with $x^3$, $x^5$ etc. so I am summing up ...
1
vote
2answers
67 views

Units in this problem: velocity or distance?

I know this is slightly off-topic here, but it's really bothering me. My class was given the following immensely simple problem today: A bird flies due south at a constant speed of ...
1
vote
1answer
88 views

The question is how many ounces (dry material) to add to one gallon of water?

The question is how many ounces (dry material) to add to one gallon of water? Formula given was 45.5g/100ml 45.5 grams (dry)= powdered sodium carbonate 100 ml (fluid)= water
1
vote
3answers
47 views

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 ...
1
vote
1answer
26 views

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 ...
1
vote
1answer
1k 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 ...
1
vote
1answer
59 views

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 ...
1
vote
1answer
34 views

How to normalise equations of the form $dy/dx=B$ and $d^2y/dx^2=A$?

So I am trying to normalise equations of the form, $$dy/dx=B \mbox{ and } d^{2}y/dx^{2}=A$$ If I define $y^{*}$ as; $$y^{*}=By \Rightarrow dy^{*}/dy=B $$ Is it also then true that, $$d(dy^{*})/dy = B ...
1
vote
1answer
48 views

cross-products versus units of measure

If I draw 2 perpendicular line segments on the ground, 3 meters and 4 meters, how far into the sky does their cross-product extend? What if instead the line lengths are 300 cm and 400 cm? Can ...
1
vote
1answer
130 views

Angular speed to linear speed: Arbitrarily discarding Radians units?

I asked this question long ago, but wanted to see if I can get some new perspectives this time. Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit. For all ...
1
vote
2answers
373 views

Convert angles from the sexagecimal system to centesimal one

How do you convert angles from the sexagecimal system to centesimal one? For example 63 degrees 14 minutes 51 seconds reduced to centesimal ?? Here's how it's done but I don't understand the ...
1
vote
1answer
1k views

Units in definite integral

I've been given a problem in my electrical engineering class which is confusing me. I'm given $i(t) = 5\sin(6 \pi t/\mathrm s)\, \mathrm{mA}$ (mA is mC/s) and I need to find the total charge ...
1
vote
1answer
170 views

What are the units of Singular Value Decomposition components?

I have a symmetric variance/covariance matrix $A$ which is of size (27 x 27). I know that it's rank deficient (rank = 21). I also know that the units of $A$ are $m^2$. I am trying to use Singular ...
1
vote
1answer
348 views

Best possible metric vs imperial conversion table?

Is there a better, smarter way of structuring a metric vs imperial conversion table than the one below? I.e. for a spreadsheet for calculating storage / shipping costs for products whose suppliers ...
1
vote
1answer
33 views

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 ...
1
vote
1answer
43 views

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:
1
vote
0answers
27 views

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 ...
1
vote
1answer
37 views

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?
0
votes
1answer
349 views

Is there a “metric system” equivalent for measuring time? [closed]

Just as in the metric system it's easy to convert from one unit of measurement to another using base 10, is there any calendaring system that measures time in an equivalent way? In other words, is ...