Question

In a laboratory, you determine that the density of a certain solid is 5.23×10−6kg/mm3. Convert this density into kilograms per cubic meters.
Notice that the units you are trying to eliminate are now in the denominator. The same principle from the previous parts applies: Pick the conversion factor so that the units cancel. The only change is that now the units you wish to cancel must appear in the numerator of the conversion factor.

Answer 1

Answer:

5,230kgm^{-3}

Explanation:

In physics, there are what we call prefix and SI units. Prefix are letters that actually denote a numerical value and this are most times appended before the SI unit of a physical quantity and SI unit is just a convention appended in the magnitude of a physical quantity so that this magnitude can be imagined. I will give quick examples, consider this magnitude of length:

200cm - it is pronounced 200 centi meter. In this case, the centi is actually a prefix denoting the value ($10^{-2}$) and the meter is the SI unit for length. So converting 200cm -> m is as simple as saying $200 \ * \ 10^{-2}$

So in this question, we want to convert $mm^{3} \ to \ m^{3}$

Now the prefix here is milli which is ($10^{-3}$) and the SI unit is meter

=> $1mm^{3} = (10^{-3} )^{3} = 10^{-9}m^{3}$

density = $\frac{5.23*10^{-6} }{10^{-9} } = 5,230kgm^{-3}$

Answer 2

Answer:

1 mm^3 = 1.0 x 10^-9 m³

Hence;

5.23 x 10^-6 kg/mm^-3 = (5.23 x 10^-6 kg)/ 1x10^-9 m³

= 5230 kg/m³