Am I cubing these units? If so how?
My thinking? decimeter =10^-1 = 0.1, centimeter 10^-2= 0.01
If 1 liter = 1 cubic decimeter, how can it also equal 1000 cubic centimeters when the two units are only separated by a factor of 10?
Can some one explain?
$\endgroup$1 Answer
$\begingroup$A decimeter is $10 \text{cm}$
so
$$(1\text{dm})^3 = (10\text{cm})^3 = 1000 \text{cm}^3 = 1 \text{L}$$
Note you are cubing not only the number 10 to get 1000 but also the unit.
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