To convert 4.56 g/cm{eq}^3{/eq} to hg/dm{eq}^3{/eq} using dimensional analysis, we can use the conversion factors 1 g = 0.01 hg and 1 cm{eq}^3{/eq} = 0.001 dm{eq}^3{/eq}.
Starting with 4.56 g/cm{eq}^3{/eq}, we can set up the following dimensional analysis:
4.56 g/cm{eq}^3{/eq} * (0.01 hg/1 g) * (1 dm{eq}^3{/eq}/0.001 cm{eq}^3{/eq})
The g unit cancels out, leaving us with units of hg/dm{eq}^3{/eq}:
4.56 * 0.01 * 1 / 0.001 = 456 hg/dm{eq}^3{/eq}
Therefore, 4.56 g/cm{eq}^3{/eq} is equivalent to 456 hg/dm{eq}^3{/eq}.
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