Something in my brain has gone horribly wrong

[Saladsamurai]

This is an extremely easy concept that for some reason is destroying my life right now.

It just came up in a physics problem that I posted elsewhere.

I have a cube of side length .6m So the area of one side is (.6)^2=
.36m^2

This does not agree with me. If it were of side length 6 then A=6^2=36.

This makes sense. 36>6. But .36<.6

Same with volume 6^3=216>6...but .6^3=.216<.6

what gives? What the hell is wrong with me/this?

Casey

 

[cristo]

It's just the units that you're using. If you think of a cube of sides 60cm, then the area of one side would be 3600cm^2. Now, converting into metres; 1m^2=(100cm)*(100cm)=10,000cm^2, so 3600cm^2=3600/10000 m^2=0.36m^2.

 

[Saladsamurai]

Maybe I need to sleep on it, but I still don't see how the number of units squared can be less than the number of units in 1 dimension.

 

[Saladsamurai]

...maybe I see it now...darn, now I have NO idea what is wrong in my physics problem

Casey

 

[Gokul43201]

It seems your question can be reduced to a problem with accepting that for all positive n, n > 1 => n² > n and n < 1 => n² < n.

Does restating your confusion in the above terms help clear some fog?

 

[Integral]

You are trying to compare .6m a length to .36m² an area. This is an apples to oranges comparison, there is no way that a length can be greater then, less then, or even equal to a length.

If you would take the time to draw a picture, I bet you will quickly agree that square .6m on a side is about 1/3 of a square 1m on a side.

 

[Gib Z]

Remember, when you square it, your units also get squared. So basically before when it only took 100 cm for 1 m, now it takes 10,000 cm^2 for 1m^2.

 

[Saladsamurai]

It seems your question can be reduced to a problem with accepting that for all positive n, n > 1 => n² > n and n < 1 => n² < n.

Does restating your confusion in the above terms help clear some fog?

Yeah. I kid got beef with that too. I am not sure why yet...but I do.
Did I just say got beef?

Casey

 

[arildno]

Multiplying a number with another number that is less than 1 yields a number less than the first.

 

[HallsofIvy]

Have you looked at a graph of y= x² lately? For x< 1, it is below the line y= x. For x> 1, it is above. Of course, the curve and line cross at (0,0) and (1,1).