Unit conversions involving Pascals

[chriscarson]

Summary:: Pascal units digits

Do somebody have a chart that converts pascals , mega pascals etc to units to know how many digits or zeros there are after the point please ?

Thanks

 

[Vanadium 50]

Theres' nothing special about pascals. Kilo is 1000, mega is 1000000 etc.

 

[chriscarson]

So for example when you have the result of 15 625 000 N m 2 how you put in pascals ? 15 625 kPa ?

Thanks

 

[etotheipi]

So for example when you have the result of 15 625 000 N m 2 how you put in pascals ? 15 625 kPa ?

Thanks

Yes, $1 \text{ Pa} = 1 \text{ N} \text{m}^{-2}$ by definition. Like @Vanadium 50 alluded to, the SI prefixes are general.

 

[A.T.]

Do somebody have a chart that converts pascals , mega pascals etc to units to know how many digits or zeros there are after the point please ?

https://en.wikipedia.org/wiki/Metric_prefix#List_of_SI_prefixes

 

[chriscarson]

https://en.wikipedia.org/wiki/Metric_prefix#List_of_SI_prefixes

Thank you

 

[chriscarson]

Yes, $1 Pa = 1 Nm^{-2}$ by definition. Like @Vanadium 50 alluded to, the SI prefixes are general.

So 1 Pa = 0.01Nm with tha little -2 ?

 

[etotheipi]

So 1 Pa = 0.01Nm with tha little -2 ?

No, $\text{N} \text{m}^{-2}$ is equivalent to $\frac{\text{N}}{\text{m}^{2}}$! It has no relevance to the prefix whatsoever!

 

[chriscarson]

No, $Nm^{-2}$ is equivalent to $N/m^{2}$! It has no relevance to the prefix whatsoever!

Ok
Thanks . Have to study more about these to understand.

 

[etotheipi]

So for example when you have the result of 15 625 000 N m 2 how you put in pascals ? 15 625 kPa ?

Thanks

You seemed like you had it here! You can think of units sort of like algebraic quantities. To do the conversion, you could write down

$15625000 \text{ N}\text{m}^{-2} = 15625 \times 10^{3} \text{ N}\text{m}^{-2} = 15625 \text{ kN}\text{m}^{-2} = 15625 \text{ kPa}$

just like you obtained. Once you get the hang of it, you'll find that you won't really need to think at all/write all of that junk out!

 

[chriscarson]

You seemed like you had it here! You can think of units sort of like algebraic quantities. To do the conversion, you could write down

$15625000 Nm^{-2} = 15625 \times 10^{3} Nm^{-2} = 15625 kNm^{-2} = 15625 kPa$

just like you obtained. Once you get the hang of it, you'll find that you won't really need to think at all/write all of that junk out!

I notice you made always a -2 on the m .

 

[Herman Trivilino]

I notice you made always a -2 on the m .

$m^{-2}=\frac{1}{m^2}$

 

[chriscarson]

$m^{-2}=\frac{1}{m^2}$

It s ok I give up . But thanks anyway for your help .

 

[vanhees71]

You seemed like you had it here! You can think of units sort of like algebraic quantities. To do the conversion, you could write down

$15625000 Nm^{-2} = 15625 \times 10^{3} Nm^{-2} = 15625 kNm^{-2} = 15625 kPa$

just like you obtained. Once you get the hang of it, you'll find that you won't really need to think at all/write all of that junk out!

And it's very important to typeset units in roman (upright), it should read
$$1 \, \text{Pa}=1 \, \text{N} \, \text{m}^{-2}=1 \, \frac{\text{N}}{\text{m}^2}$$
etc.

 

[etotheipi]

And it's very important to typeset units in roman (upright), it should read
$$1 \, \text{Pa}=1 \, \text{N} \, \text{m}^{-2}=1 \, \frac{\text{N}}{\text{m}^2}$$
etc.

Ah that's useful, never knew \text{} was a thing! My latex is dreadful...

 

[jtbell]

$m^{-2}=\frac{1}{m^2}$

It s ok I give up . But thanks anyway for your help .

Have you never seen negative exponents used to indicate reciprocals? $$10^{-2}=\frac 1 {10^2} = \frac 1 {100}$$ $$x^{-3} = \frac 1 {x^3}$$ etc.

 

[chriscarson]

Have you never seen negative exponents used to indicate reciprocals? $$10^{-2}=\frac 1 {10^2} = \frac 1 {100}$$ $$x^{-3} = \frac 1 {x^3}$$ etc.

No . I finished school early now I m taking a course .

 

[jbriggs444]

No . I finished school early now I m taking a course .

The meaning for negative exponents follows naturally from the law of exponents:$$x^{a+b}=x^a \times x^b$$
If you have an exponent $-a$, it then follows that:$$x^{-a} \times x^a = x^{-a+a} = x^0$$ By definition^(*), $x^0=1$ so we can write: $$x^{-a} \times x^a = 1$$ If we divide through by $x^a$ that yields: $$x^{-a} = \frac{1}{x^a}$$

(*) One might quibble about the grounding definitions for exponentiation. But I like to start with the idea that an empty product yields the multiplicative identity (1) just like an empty sum yields the additive identity (0).

 

[chriscarson]

The meaning for negative exponents follows naturally from the law of exponents:$$x^{a+b}=x^a \times x^b$$
If you have an exponent $-a$, it then follows that:$$x^{-a} \times x^a = x^{-a+a} = x^0$$ By definition^(*), $x^0=1$ so we can write: $$x^{-a} \times x^a = 1$$ If we divide through by $x^a$ that yields: $$x^{-a} = \frac{1}{x^a}$$

(*) One might quibble about the grounding definitions for exponentiation. But I like to start with the idea that an empty product yields the multiplicative identity (1) just like an empty sum yields the additive identity (0).

I will need a very basic lesson to understand this . I started from the middle of the subject. but thanks

 

[jbriggs444]

I will need a very basic lesson to understand this . I started from the middle of the subject. but thanks

You could start with Wiki. Though a textbook might be better.

 

[chriscarson]

You could start with Wiki. Though a textbook might be better.

I will but I m focusing on what the exams will be about and we stopped to work out stress , strain, and young modulus because it s an assistant technician course.

 

[Herman Trivilino]

So for example when you have the result of 15 625 000 N m 2 how you put in pascals ? 15 625 kPa ?

First of all it would be 15 625 000 N/m². That's 15 625 000 Newtons of force on each square meter of area. This would be, by definition, 15 625 000 Pa. And since there are 1000 pascals in a kilopascal, it would be equivalent to 15 625 kPa.

 

[chriscarson]

this one it s ok i fully understood it

 

[Vanadium 50]

I will but I m focusing on what the exams will be about and we stopped to work out stress , strain, and young modulus because it s an assistant technician course.

Yes, but they will expect you to understand unit prefixes and exponents. What you are learning builds upon them. Knowledge is cumulative. If you have a gap, it will come up again and again until it's filled.

 

[chriscarson]

Yes, but they will expect you to understand unit prefixes and exponents. What you are learning builds upon them. Knowledge is cumulative. If you have a gap, it will come up again and again until it's filled.

Yes it s true

 

[chriscarson]

Some thing more I met and can t find the mistake is,when finding the area of a circle with 25 mm radius.
When calculating in mm the result is 1964 mm
When calculating in m the result is 0.00196375 m

When converting 0.00196375 m to mm it gives me 1.96375 m not as the first result of 1964 mm

 

[jbriggs444]

Some thing more I met and can t find the mistake is,when finding the area of a circle with 25 mm radius.
When calculating in mm the result is 1964 mm
When calculating in m the result is 0.00196375 m

When converting 0.00196375 m to mm it gives me 1.96375 m not as the first result of 1964 mm

An area should be expressed using a unit of area, such as square meters or square millimeters.

The conversion factor between square millimeters and square meters is 1,000,000.

 

[chriscarson]

An area should be expressed using a unit of area, such as square meters or square millimeters.

The conversion factor between square millimeters and square meters is 1,000,000.

An area should be expressed using a unit of area, such as square meters or square millimeters.

The conversion factor between square millimeters and square meters is 1,000,000.

So it s true to have different result ?

 

[chriscarson]

So it s true to have different result ? And the 0.00196375 m squared is ok in exams ?

 

[Herman Trivilino]

Some thing more I met and can t find the mistake is,when finding the area of a circle with 25 mm radius.
When calculating in mm the result is 1964 mm
When calculating in m the result is 0.00196375 m

Try it this way: $\pi r^2 = \pi (0.025 \ \text{m})^2$.

 

[chriscarson]

Try it this way: πr2=π(0.025 m)2πr2=π(0.025 m)2.

That s exactly what I did

 

[jbriggs444]

That s exactly what I did

But you messed up the units. Note that @Mister T suggested you carry the units in the calculation.$$\pi \times 0.025 \text{m} \times 0.025 \text{m} = 0.0019635 \text{m}^2$$Which is different from$$0.0019635\text{m}$$

 

[chriscarson]

But you messed up the units. Note that @Mister T suggested you carry the units in the calculation.$$\pi \times 0.025 \text{m} \times 0.025 \text{m} = 0.0019635 \text{m}^2$$Which is different from$$0.0019635\text{m}$$

yes apart of the units , the answer is 0.00196375 m 2 , is it acceptable in an exam ?

 

[jbriggs444]

yes apart of the units , the answer is 0.00196375 m 2 , is it acceptable in an exam ?

Yes, almost certainly. The units I would expect area to be reported in would be square meters.

However... The rules for significant figures suggest that less precision should be reported. And the calculated result you give is incorrect in the last two digits.

 

[chriscarson]

Yes, almost certainly. The units I would expect area to be reported in would be square meters.

Ok . thanks again

 

[jbriggs444]

Ok . thanks again

Note the caveats I've edited into the previous post.

 

[chriscarson]

Yes, almost certainly. The units I would expect area to be reported in would be square meters.

However... The rules for significant figures suggest that less precision should be reported. And the calculated result you give is incorrect in the last two digits.

I did , 0.025m x 0.025m = 0.000625 m2

0.000625 x 3.142 = 0.00196375m2

 

[jbriggs444]

I did , 0.025m x 0.025m = 0.000625 m2

0.000625 x 3.142 = 0.00196375m2

$\pi$ is not equal to 3.142 -- at least not to the six significant figures that you quoted in the result.

 

[chriscarson]

$\pi$ is not equal to 3.142 -- at least not to the six significant figures that you quoted in the result.

so that could be were I m mistaken ?

 

[chriscarson]

$\pi$ is not equal to 3.142 -- at least not to the six significant figures that you quoted in the result.

so that could be were I m mistaken ?

 

[jbriggs444]

so that could be were I m mistaken ?

You've not told us that someone told you that you were mistaken. We are not mind readers.

 

[chriscarson]

You've not told us that someone told you that you were mistaken. We are not mind readers.

I mean I am asking if it is that what I am doing wrong. If it is because I am using only till 3.142 than 6 significant figures.

 

[jbriggs444]

I mean I am asking if it is that what I am doing wrong. If it is because I am using only till 3.142 than 6 significant figures.

When in doubt, check it out.

Let us make three attempts at the calculation. One using the truncated figure for $\pi$, one using a value of pi that is good for six figures and one using a value that is good for as much as Windows calculator will do.

$\pi$ is approximately 3.141_592_653_589_793_238_462_6. Usually, people remember it to three digits (3.14) because the next digit is a one and it's a no brainer to round 3.141 down to 3.14. Often people remember it to 5 digits (3.1416) because the next digit is a nine and it's a no brainer to round 3.14159 up to 3.1416. However, you have chosen to remember it to 4 digits (3.142), rounding 3.1415 up to 3.142. That's a remarkably poor place to truncate the decimal expansion since it was nearly a 50/50 choice to round up or down, given that the first truncated digit was a five.

On to the checking out part...

Four digit calculation: 3.142 x 0.025²: Calculator says 0.00196375. Rounded to six significant figures, that is still 0.00196375. Rounded to two significant figures, it is 0.0020.

Six digit calculation: 3.14159 x 0.025²: Calculator says 0.00196349375. Rounded to six significant figures, that is 0.00196349. Rounded to two significant figures, it is 0.0020.

My windows calculator limit: 3.1415926535897932384626433832795 x 0.025²: Calculator says 0.00196349540849362077403915211455. Rounded to six significant figures, that is 0.00196350. Rounded to two significant figures, it is 0.0020.

Note how the last two digits in the six figure result changed depending on the accuracy of the figure used for pi. Note how the last digit in the six figure result was incorrect even though the calculation used a value for pi that was good to six digits.

1. If you are going to use a defined constant, use it with all available precision.
2. If you are going to compute an intermediate result, use all available precision.
3. When you report a final result, round it to the appropriate number of significant figures. In this case, with inputs good to two significant figures, the result should have been reported to two digits or certainly no more than three.

These rules of thumb will get you through at least freshman physics. Real numerical analysis and error analysis goes way deeper.

 

[chriscarson]

thanks for your time I will study more to what you wrote , it will help for sure.

So from you wrote , the best thing is that they tell you to how many numbers should be rounded , the pi and the answer.

 

[chriscarson]

When you make 3.14 x ( 0.025m x 0.025m) = 0.0019625m2 converted to mm is 1.9625mm2

and if you make 3.14 x ( 25mm x 25mm ) = 1962.5mm2 converted to m is 1.9625m2

I think it s a matter when you convert or in the question or in the answer . Results are different.

 

[jbriggs444]

When you make 3.14 x ( 0.025m x 0.025m) = 0.0019625m2 converted to mm is 1.9625mm2

No, it is not.

As I'd already pointed out in post #27, the conversion factor between square meters and square millimeters is 1,000,000. There are one million squares, one millimeter on a side in a square that is one meter on a side.

You are not converting from meters to millimeters. You are converting from square meters to square millimeters.

$$0.0019625 \text{ m}^2 \times \frac{1,000,000 \text{ mm}^2}{1 \text{ m}^2} = 1962.5 \text{ mm}^2$$

I am running out of different ways to say this.

 

[chriscarson]

No, it is not.

As I'd already pointed out in post #27, the conversion factor between square meters and square millimeters is 1,000,000. There are one million squares, one millimeter on a side in a square that is one meter on a side.

You are not converting from meters to millimeters. You are converting from square meters to square millimeters.

$$0.0019625 \text{ m}^2 \times \frac{1,000,000 \text{ mm}^2}{1 \text{ m}^2} = 1962.5 \text{ mm}^2$$

oh I think I get it now so the best is convert in the question , because they told me that the answer have to be in Newtons and meters.

 

[jbriggs444]

oh I think I get it now so the best is convert in the question , because they told me that the answer have to be in Newtons and meters.

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.

 

[berkeman]

because they told me that the answer have to be in Newtons and meters.

Who is "they"? Has this been for your homework all along?

 

[chriscarson]

Who is "they"? Has this been for your homework all along?

The teacher said you have always to give the result in N/m2 (Newton meter squared)