Math Is Fun Forum

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.

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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)

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

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

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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