Why is a $1dm^3$ volume equivalent to $1L$ ?

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Answer 1 · 2016-10-03T16:55:00

$1*dm^3-=1*L-=1000*cm^3-=10^-3*m^3$ .

$d$ is the abbreviation for $"deci"=10^-1$ .

Thus $1*dm^3$ $=$ $(1xx10^-1*m)^3$ $=$ $1xx10^(-3)*m^3$

$c$ is the abbreviation for $"centi"=10^-2$ .

And $1*cm^3$ $=$ $(1xx10^-2*m)^3$ $=$ $1xx10^(-6)*m^3$

And thus there are $1000*cm^3*dm^-3$ , or $1000*cm^3*L^-1$

And there are also $1000*L*m^-3$ . A $"cubic metre"$ is a very large volume.

And thus $1*mol*dm^-3$ $=$ $1*mol*L^-1$ , which is the familiar unit of concentration.

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Why is a 1*dm^31*dm^3 volume equivalent to 1*L1*L?