# math quest

February 2, 2012 7:16 PM Subscribe

Ask MathaFilter:
If I square 100 mm I get 10,000 mm.
But, convert to .1 m, and square, we have .01, a smaller amount!
Why can using a conversion like this give a nonsensical answer? If I want a length times itself why does it matter the metric?

Best answer: If you square 100 mm you get 10,000 mm^2 (not mm). If you square 0.1 m you get 0.01 m^2 (not m). Those are the same amount.

A square meter has a million square millimeters in it, not a thousand.

posted by stebulus at 7:22 PM on February 2, 2012 [1 favorite]

A square meter has a million square millimeters in it, not a thousand.

posted by stebulus at 7:22 PM on February 2, 2012 [1 favorite]

Best answer: Because you don't get 10,000 mm. You get 10,000 SQUARE mm, which is a different thing entirely. When you say "We have .01, a smaller amount", you are doing that by converting back to mm. But you can't convert .01 SQUARE metres into SQUARE mm by multiplying by 1000.

posted by lollusc at 7:22 PM on February 2, 2012 [2 favorites]

posted by lollusc at 7:22 PM on February 2, 2012 [2 favorites]

One thing I do with my students that helps with this sort of thing is to take a meter stick and draw out a square meter. Then draw a square centimeter. Suddenly, the idea that there aren't 100 cm

posted by Dr.Enormous at 7:34 PM on February 2, 2012 [1 favorite]

^{2}in 1 m^{2}becomes a lot more obvious, as does the idea that we have to alter the conversion factor accordingly (square the 100 too, basically).posted by Dr.Enormous at 7:34 PM on February 2, 2012 [1 favorite]

Also, squaring something just means multiplying it by itself. Any number

posted by LionIndex at 7:42 PM on February 2, 2012

*n*multiplied by one equals the original number*n*. Multiplying by a number larger than one results in a number larger than*n*, so it makes sense that multiplying by a number smaller than one would result in a number smaller than*n*.posted by LionIndex at 7:42 PM on February 2, 2012

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bothsides of the equation. If you square 100 mm you get 10,000 mm^2 (that's ten thousand square millimeters). If you square .1 m you get .01 m^2 (that's one hundredth of a square meter). But because there are a million square millmeters in a square meter, those are the same thing!posted by willbaude at 7:21 PM on February 2, 2012 [8 favorites]