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

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

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

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).

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

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

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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