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]

there's' 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: $\pi r^2 = \pi (0.025 \ \text{m})^2$.