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I don't know why I always have trouble with these things, there is something that must do 'click' in my head.

Knowing that 1000000 cm³ = 1 m³, how do you get that 

    cm³
-----------
 0,000001 m³`?

It is pretty obvious visually that 1 cm³ = 0,000001 m³, but how to do it matematically? It is for unit conversion.

1000000 cm³ = 1 m³

   1 cm³ = 1 m³
          ------
           1000000

then

1 =    1 m³
      ------      Now i'm lost!
       1000000
    ---------- 
        cm³
tpb261
  • 802
JorgeeFG
  • 493
  • though I don't see where you might be confused, your last statement should be $ 1 = \left(\frac{1m^3}{1000000}\right)/(1cm^3)$ Also, 1m=100cm, so change accordingly – tpb261 May 27 '14 at 05:53
  • @tpb261 I am confused in how to get to cm³ above 0,000001 m³ – JorgeeFG May 27 '14 at 05:58
  • I think you are trying to solve some other problem, if that is the case, you can replace all $cm^3$ with $0.000001 m^3$ or $m^3$ with $1000000 cm^3$ – tpb261 May 27 '14 at 06:08

1 Answers1

1

Problem is 1000 cm³ = 1 m³ is FALSE.

1 m = 100 cm

so

1 m³ = (100 cm)³ = 1000000 cm³
CiaPan
  • 13,049
  • Thanks, thats a good spot, but how do you get to cm³ / 0,000001 m³ ? I need it that way so I can cancel cm³ with cm³ when converting units – JorgeeFG May 27 '14 at 05:57
  • In arithmetics you just handle a unit as a separate term in multiplication. So if we say 1m=100cm we can divide both sides of the equation by 1m to get 1=(100cm)/(1m). You can raise both sides to a power: (1)³=((100cm)/(1m))³ which results in 1=(100cm)³/(1m)³ = (100³ cm³)/(m³) = 1000000 cm³/m³. You can, of course, also multiply enumerator and denominator by the same value, say 1/1000000, so finally 1 = (1 cm³)/(0,000001 m³). – CiaPan May 27 '14 at 06:12
  • Thanks, thats what I was needing, a dumb-proof exaplanation – JorgeeFG May 27 '14 at 06:27