#### Answer

There are 1000 cubic decimeters in one cubic meter.

#### Work Step by Step

We know that $1~m = 10~dm$
We can find the number of cubic decimeters in one cubic meter.
$1~m^3 = 1~m\times 1~m\times 1~m$
$1~m^3 = 10~dm\times 10~dm\times 10~dm$
$1~m^3 = 1000~dm^3$
There are 1000 cubic decimeters in one cubic meter. Note that a cubic meter has three dimensions so we need to multiply the conversion factor three times.