Understanding Orders of Magnitude: Clearing Up Confusion | Homework Help

[liamporter1702]

Homework Statement

Hi guys this isn't so much a coursework or homework help problem but figured this would be a sensible place to post my question. Basically I got back an assignment I had recently completed from my tutor and I had been marked down for some errors in regard to the orders of magnitude and he said I have been using the same order of magnitude for let's say μm (10^-6) as μm^2. My question is, what is the difference when the units are squared? Does this mean that, let's say 8μm^2 would not be equal to 8x10^-6 but a different value? Any help is appreciated to clear this up

 

[jbunniii]

Consider a square with side lengths equal to ##1 \mu m = 10^{-6}m##. Try expressing the area of this square in ##\mu m^2## and in ##m^2##.

 

[liamporter1702]

Would this be correct:

For area in μm = 1μm^2

and area in m = 10^-6m^2

Thanks for replying!

 

[jbunniii]

Would this be correct:

For area in μm = 1μm^2

Yes.

and area in m = 10^-6m^2

No. If the side length is ##10^{-6}m##, then what do you get when you square that? Surely the square of ##10^{-6}## is not ##10^{-6}##.

 

[liamporter1702]

Ah I see! It would be 10^-12?

 

[dauto]

Homework Statement

Hi guys this isn't so much a coursework or homework help problem but figured this would be a sensible place to post my question. Basically I got back an assignment I had recently completed from my tutor and I had been marked down for some errors in regard to the orders of magnitude and he said I have been using the same order of magnitude for let's say μm (10^-6) as μm^2. My question is, what is the difference when the units are squared? Does this mean that, let's say 8μm^2 would not be equal to 8x10^-6 but a different value? Any help is appreciated to clear this up

The conversion factor must also be squared - obviously. Draw a square 10cm by side on a piece of paper. Cut it down to squares 1cm by 1 cm (Don't really cut, just draw them). How many little squares do you have at hand? Do you have only 10 little squares?

 

[jbunniii]

Ah I see! It would be 10^-12?

That's right. So ##1 \mu m^2 = 10^{-12} m^2##, not ##10^{-6}m^2##.