Convert the following (using conversion factors): \( 400,000 \mathrm{~mm}^{3}=\square \mathrm{dm}^{3} \)

To convert cubic millimeters to cubic decimeters, you'll want to know that \(1 \, \mathrm{dm}^3 = 1,000,000 \, \mathrm{mm}^3\). Thus, you can set up the conversion as follows: \[ 400,000 \, \mathrm{mm}^3 \times \frac{1 \, \mathrm{dm}^3}{1,000,000 \, \mathrm{mm}^3} = 0.4 \, \mathrm{dm}^3 \] So, \(400,000 \mathrm{~mm}^{3} = 0.4 \mathrm{dm}^{3}\). When working on unit conversions, it’s always helpful to write out what you know and watch how the units cancel out—that way, you avoid pitfalls like mixing up your dimensions!