Unit conversions involving Pascals

[chriscarson]

Given an input measurement of 25 millimeters radius and desiring a result for the area of a corresponding circle, there are two ways to proceed.

1. Convert 25 millimeters to meters and compute $\pi r^2$ with the result in square meters.
2. Compute $\pi r^2$ with the result in square millimeters and convert the result to square meters.

Let us proceed with the first approach.
$$r=25\text{ mm} \times \frac{1\text{ m}}{1000\text{ mm}}=0.025\text{m}$$ $$a=\pi r^2=\pi (0.025\text{ m})^2=0.0019635\text{ m}^2$$ Round to 0.0020 m²Let us try the second approach instead.
$$r=25\text{ mm}$$ $$a=\pi r^2=\pi\ (25\text{ mm})^2=1963.5\text{ mm}^2=1963.5\text{ mm}^2 \times (\frac{1\text{ m}}{1000\text{ mm}})^2=\frac{1963.5}{1000 \times 1000}\text{ m}^2 = 0.0019635\text{ m}^2$$ Round to 0.0020 m²

Six of one. Half dozen of the other.

Ok so you did convert from square mm to square m but in the proper way , I used an online converter.

 

[chriscarson]

I always stop to something when I try to make a sum , this time I have this to make me confuse , same exactly sum but different calculators different results .

 

[Ibix]

That's the same result, just written in a different format. The e-5 at the end of the first number is a standard computer and calculator way of writing $×10^{-5}$. So that number is $3.333×10^{-5}$, which is $3.333×\frac 1{10^5}$ or $3.333×\frac 1{100,000}$ or 0.00003333, which is what the other calculator says.

 

[chriscarson]

That's the same result, just written in a different format. The e-5 at the end of the first number is a standard computer and calculator way of writing $×10^{-5}$. So that number is $3.333×10^{-5}$, which is $3.333×\frac 1{10^5}$ or $3.333×\frac 1{100,000}$ or 0.00003333, which is what the other calculator says.

Oh so much to learn I guess .
Thanks

 

[Ibix]

Oh so much to learn I guess .
Thanks

This stuff is like learning where to put your fingers on a guitar or something. It's slow going and you get a lot of nasty sounds, but you have to learn it if you want to play. It does eventually become second nature and it's really difficult to remember not knowing how to do it.

 

[chriscarson]

This stuff is like learning where to put your fingers on a guitar or something. It's slow going and you get a lot of nasty sounds, but you have to learn it if you want to play. It does eventually become second nature and it's really difficult to remember not knowing how to do it.

great simplification of what you mean. going to keep this quote to motivate who s going to give up, well done

 

[chriscarson]

And it keeps going with strange things, last question is to find the young modulus , in the notes if found this to confuse me , E is equal to two different formulas

 

[A.T.]

E is equal to two different formulas

Use the one for which you have the required variables.

 

[Ibix]

Note that the $x$ in the second formula should be the multiplication symbol ×.

Stress is force over area. Strain is length change over original length. The second formula is what you get when you substitute those definitions into the first formula.

 

[jbriggs444]

Ok so you did convert from square mm to square m but in the proper way , I used an online converter.

Online converters work. Just have to use the right units. I Googled "convert square millimeters to square meters". Without leaving the Google page, a converter was displayed. I keyed in 1963.5.

 

[chriscarson]

Online converters work. Just have to use the right units. I Googled "convert square millimeters to square meters". Without leaving the Google page, a converter was displayed. I keyed in 1963.5.
View attachment 255555

Good nit saying that it s an area value it was a mistake

 

[chriscarson]

Use the one for which you have the required variables.

Yeah and is it that you multiply first or work the division separated and the multiply the results ?

 

[jbriggs444]

Yeah and is it that you multiply first or work the division separated and the multiply the results ?

Multiply what by what or work what division? Are you seriously asking how to evaluate $\frac{a}{b} \times \frac{c}{d}$?

 

[chriscarson]

Multiply what by what or work what division? Are you seriously asking how to evaluate $\frac{a}{b} \times \frac{c}{d}$?

Yes is that so basic ?

 

[jbriggs444]

Yes is that so basic ?

Here in the U.S. we are taught to add and multiply fractions at about age eight.

For $\frac{a}{b} \times \frac{c}{d}$ there are many ways to evaluate the result and get the same right answer. The canonical "right" way is to:

1. Divide a by b giving the result $\frac{a}{b}$.
2. Divide c by d giving the result $\frac{c}{d}$.
3. Multiply those two results together.

Another way is to:

1. Multiply a by c giving the result $ac$.
2. Multiply b by d giving the result $bd$.
3. Divide the result from 1) by the result from 2).

It is a rule of arithmetic and of real algebra that$$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$

One rule of algebra that they didn't teach us until age 16 or so was that putting two variable names side by side ("juxtaposition") is a notation that conventionally means "multiply them together".

[As it turns out my first exposure to the juxtaposition notation was in a standardized test -- they tested on it before my school had ever presented the content. It is over 40 years later now and that incident still cheeses me off]

 

[chriscarson]

Here in the U.S. we are taught to add and multiply fractions at about age eight.

For $\frac{a}{b} \times \frac{c}{d}$ there are many ways to evaluate the result and get the same right answer. The canonical "right" way is to:

1. Divide a by b giving the result $\frac{a}{b}$.
2. Divide c by d giving the result $\frac{c}{d}$.
3. Multiply those two results together.

Another way is to:

1. Multiply a by c giving the result $ac$.
2. Multiply b by d giving the result $bd$.
3. Divide the result from 1) by the result from 2).

It is a rule of arithmetic and of real algebra that$$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$

One rule of algebra that they didn't teach us until age 16 or so was that putting two variable names side by side ("juxtaposition") is a notation that conventionally means "multiply them together".

[As it turns out my first exposure to the juxtaposition notation was in a standardized test -- they tested on it before my school had ever presented the content. It is over 40 years later now and that incident still cheeses me off]

Yeah finally is that what I thought but I m finding so many obstacles that I want to be 100% in every tiny thing .

 

[scottdave]

Maybe I missed it in the thread, but this chart of metric prefixes and corresponding powers of ten may come in handy for you. http://www.ibiblio.org/units/prefixes.html

 

[chriscarson]

Maybe I missed it in the thread, but this chart of metric prefixes and corresponding powers of ten may come in handy for you. http://www.ibiblio.org/units/prefixes.html

Thanks for the help