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#1 2005-08-31 08:34:02

Wladislaw
Member
Registered: 2005-08-31
Posts: 1

Dimensional Arrays?

In my physics class, my teacher introduced me to dimensional arrays, but explained them very poorly; naturally, I was hoping you could help me.
array.gif
This is the problem I need help with.  It's purpose was to convert a light year into inches, and LY stands for light year.  Could someone tell me how the problem is solved to get 3x10^17 inches, and the process they took?

Thanks in advance,
Wladislaw

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#2 2005-08-31 10:04:17

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

Re: Dimensional Arrays?

here's what I found:

1) multiply all numerators and divide by all denominators

(1 LY * 9.46E15m * 100cm * 1 in )
----------------------------------------
      ( 1 * LY * m * 2.54 cm )

2) you can "cut" (do you say "cancel"??) LY's ; m's and cm
   see how the final unit doesn't disapear

(1 * 9.46E15 * 100 * 1 in )
-----------------------------------
          ( 1 * 2.54 )

3) obvious stuff

9.46E17
---------  in
  2.54

wich is aproximately...
3E17 in


but please check it in your textbook beacause I never used this in physics. I found the solution by logic...
Until now I have never heard of such technique "dimentional arrays". But in the end it's just a bunch of proportions (fractions).

smile

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#3 2005-08-31 10:40:06

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,551

Re: Dimensional Arrays?

Yeah, "dimensional arrays" sounds too much of a mouthful for something so simple.

As kylekatarn showed, it is only cancelling of terms in a fraction.

For example LY to m is:

1 LY  ×  (9.46 × 10^15 m/LY) = (1 × 9.46 × 10^15 mLY/LY) = 9.46 × 10^15 mLY/LY

So the result has the units mLY/LY which is just m, because LY/LY can be cancelled (I think the interpretation of LY/LY is "Light-Years per Light Year" which is of course 1)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2005-08-31 13:21:50

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: Dimensional Arrays?

Or another example would be to convert one foot into 12 inches.

(1 foot/1) multiplied by (12 inches/foot)

The foot in the numerator cancels with the foot in the denominator, so the units of the answer is inches.


igloo myrtilles fourmis

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