For questions related to conversion of units.

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16
votes
8answers
4k 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 ...
7
votes
4answers
239 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 ...
5
votes
2answers
758 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 ...
4
votes
5answers
606 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 ...
4
votes
4answers
10k 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 ...
3
votes
3answers
129 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
176 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
107 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
1k 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
199 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
302 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
155 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
61 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
166 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
1answer
21 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
106 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
191 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
94 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
107 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
1k 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
22 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
35 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
45 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
61 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
69 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
1answer
42 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
25 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
29 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
78 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
145 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
903 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
134 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
317 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
0answers
13 views

Nondimensionalisation - does it always reduce the number of parameters?

I've just made my ODE system of 8 equations dimensionless, but I've come out with exactly the same number of dimensionless parameters as I had in the system with units. Can nondimensionalisation ...
1
vote
1answer
30 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
317 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 ...
0
votes
1answer
79 views

Question on bel and decibel?

What do these units of measurement mean? In Analogue Electronic class, the Prof uses $20 \log_{10}$ and in my Networks and Protocols class, the Prof uses $10 \log_{10}$ but they both refer ...
0
votes
4answers
79 views

A Time Calculation Problem: 3yrs or 3yrs and 1 day?

Suppose, a person A has his birthday on 30 Sept 1994 and another person B has his birthday on 30 Sept 1997, then which of the following statement would be correct and why? The difference between the ...
0
votes
1answer
24 views

english to metric conversion with cubes

How do you convert $ft^3$ to $cm^3$? I can find an exact relationship online, but what if I just knew how many $m$ are in a $lb$ or something like that?
0
votes
2answers
49 views

Conversion of dosage based on body weight

Infant ibuprofen containes 100mg/5.0mL suspension. The recommended dose is 10mg/kg body to weight. How many mL of this suspension should be given to an infant weighing 18 lb? That's not a serious ...
0
votes
1answer
36 views

D=P/gv^3 what units is the D

(Sorry for my bad english) I got a task to do: In the research, scientists noticed that the necessary power P is obtained from P=Dgv^3, where D is constant, g is the earth's standard acceleration ...
0
votes
2answers
126 views

Converting squared or cubed units

At the moment I am going from square meters to square yards. One meter is $1.0936$ yards. So I figure $1\text{m}^2 = 1.0936 \text{yards}^2$ I know it isn't but I want to learn a good systematic ...
0
votes
1answer
33 views

How do you figure out the formula to convert between units?

I know that to, for example, convert from Fahrenheit to Celsius you subtract 32 and then divide by 1.8. I'm interested in how this type of formula can be developed. So, given two different sets of ...
0
votes
1answer
53 views

If the cost per minute is $\$0.032$, is the cost per hour $\$1.92$ or $1.92$¢?

I hope someone can help me with this problem. The cost per minute to make a phone call is $0.032, I'm that multiplying this by 60 will get total cost per hour. ...
0
votes
2answers
75 views

How many inches are in 7.94 feet?

Question: the height on my land is 7.94 feet noted by a surveyor on a Certificate of Elevation form. In layman's terms, that is 7 feet and how many inches? or how much of an inch is it short of 8 ...
0
votes
1answer
22 views

Find total yards with LXWXH?

I have a box I need to cover all 6 sides with a single layer fiberglass fabric. The fabric comes in 50" or 28" widths. The dimensions of the box are 34" long; 15" wide; 12" High. How do I determine ...
0
votes
1answer
50 views

sub-nanoseconds resolution

I found following statement in a higher engineering mathematics reference book, But couldn't understand how it has been determined ? I have two values as follows: nanoseconds - could be any 30 ...
0
votes
1answer
30 views

I have trouble understanding simple equality passage

I don't know why I always have trouble with these things, there is something that must do 'click' in my head. Knowing that 1000000 cm³ = 1 m³, how do you get that ...
0
votes
1answer
26 views

How many gallons are used in the U.S. each day and if this gasoline were used to fill a cubical tank how big would one side be?

The question I am trying to solve is: Part I) How many gallons of gasoline are used in the U.S. in one day assuming there are $2$ cars for every $3$ people and each car is driven $10,000$ miles a ...
0
votes
2answers
47 views

How to change to same units

Could anyone help me change it into same units/ values? I need to have them all in "years" Demand(D): Every month there is 5000 food: Therefore, $D= 5000 * 12 = 60000$ food per year Production(P): ...