Question

a laboratory, you determine that the density of a certain solid is 5.23×10−6kg/mm3. Convert this density into kilograms per cubic meter. 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

`5.23* 10^(-6)\ kg/mm^3=5230\ kg/m^3`

Explanation:

Given : The density of a certain solid is
`5.23* 10^(-6)` kg/mm³.

To find : Convert this density into kilograms per cubic meter ?

Solution :

We know that,

`1\ m^3=10^9\ mm^3`

or
`10^9\ mm^3=1\ m^3`

So,
`1 mm^3=(1)/(10^9)\ m^3`

`1 mm^3=10^(-9)\ m^3`

Converting
`5.23* 10^(-6)` kg/mm³ into kg/m³,

`5.23* 10^(-6)\ kg/mm^3=(5.23* 10^(-6))/(10^(-9))\ kg/m^3`

`5.23* 10^(-6)\ kg/mm^3=5.23* 10^(-6+9)\ kg/m^3`

`5.23* 10^(-6)\ kg/mm^3=5.23* 10^(3)\ kg/m^3`

`5.23* 10^(-6)\ kg/mm^3=5230\ kg/m^3`

Therefore,
`5.23* 10^(-6)\ kg/mm^3=5230\ kg/m^3`