The prefix "deci"-=10^-1deci≡10−1. The prefix "centi"-=10^-2centi≡10−2. The prefix "milli"-==10^-3milli≡=10−3. And going the other way, the prefix "kilo"-=10^3kilo≡103, and the prefix "mega"-=10^6mega≡106.
And so 1*dm-=1xx10^-1xx1000*mm-=100*mm-=10*cm1⋅dm≡1×10−1×1000⋅mm≡100⋅mm≡10⋅cm.
We use 1*dm^3-=(10^-1*m)^3-=1/1000*m^3-=1*L1⋅dm3≡(10−1⋅m)3≡11000⋅m3≡1⋅L as a convenient measurement of volume.