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#1 2005-09-01 06:34:02
- Wladislaw
- Novice
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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.
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
#2 2005-09-01 08:04:17
- kylekatarn
- Power Member
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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).
#3 2005-09-01 08:40:06
- MathsIsFun
- Administrator
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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
#4 2005-09-01 11:21:50
- John E. Franklin
- Star Member
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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.
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