Hello, Correnna,
This is a problem that requires conversion factors to put everything into the final units desired. The problem doesn't specify the units for the density, but I will use grams/cm3 since that is a common unit. I could have chosen any units involving mass and volume, since density is defined as mass/volume. Volume can be m3, ml, in3, etc.
We see that all three measures of the item's dimensions are in different metric units of decimeter (dm), millimeter (mm), and hectameter (hm). Please refer to a standard metric conversion chart to see how these relate to each other.
Set up a table to keep things organized. I placed the three dimensions into the first three rows and conversion factors in the next three. Since volume is the product of width, length and height, we need to change the disparate units to just one. I decided, for now, to convert all the length measures to meters.
I've noted their relationships in lines 4 - 6 as they pertain to meters, the stand SI unit for length.
I can't get the table to fit. Please find it at: https://docs.google.com/spreadsheets/d/1KRn9PGcS2ivorrCXgfN1MuQ8NQ7hkEGezXuRZ90qGWM/edit?usp=sharing
I converted each of the three dimensions to units of meters, using lines 4 - 6 as conversion factors (shown in the right column). Simply take the unit you want to convert, such as hectameters, and multiply it by the appropriate factor. In this case, use line 6 and arrange it as:
1E+02 m/hm (which means 100 meters = 1 hectameter)
and then multiply it times the length in line three. The hm cancel and we are left with meters. That result, and the rest, are in the chart with the unit of m.
Next, just multiply all three dimensions to get the volume in units of m3. At this point, we could legally simply divide the mass by the volume in m3, but the result is barely recognizable since we have so little mass and a term of m3 that is large in comparison. Since most densities are expressed as g/ml or g/cm3, I decide to convert the m3 to cm3. This is done, again, using the conversion factors (line 9). The final result is expressed as g/cm3. We only have 3 sig figs, so it rounds nicely to 100 g/cm3. (Another good sign we've done the right thing. How likely is it that so many nasty numbers could wind up with the answer "1?"
I hope this helps. Practice using conversion factors, and always have a metric conversion table nearby to check the definitions of the abbreviations (like hectometer). You'll remember them soon enough, and look forward to using the interesting ones, such as atto- and nano- ).
I hope this helps,
Bob
