Question

Question #96eb8

Answer 1

`500 "kg"/m^3`

Explanation:

Density in the International System of Units (SI) is measured in `"kg"/m^3` ,"kilogram per cubic metre"

`0.5g/m^3 -> 500 "kg"/m^3`

Answer 2

In the S.I. units for density, `"0.5g"/"cm"^3 = 500 (kg)/m^3`

Explanation:

Please use this link to see an explanation of the method for unit conversions that I will use in my answer to you.
https://socratic.org/questions/a-mile-is-5280-ft-long-1-ft-is-approximately-0-305-m-how-many-meters-are-there-i#469538

The S.I. units for density is `"kg"/m^3`. Starting with `"0.5g"/"cm"^3`, I will show the steps to convert to `"kg"/m^3`. Note that since the centimeters are cubed, the conversion factors for length will also need to be cubed. As follows:

`(0.5g)/(cm^3) * (1 kg)/(1000 g) * (100 cm)/(1 m^3)`

Because dealing with the exponents can get complicated, I will next convert the 100 and 1000 to `10^2 and 10^3` respectively. And from there I will deal with those exponents and cancel where possible to finally get to the required result.

`(0.5 g) / (cm^3) * (1 kg) / (10^3 g) * (10^2 cm)/(1 m^3)`

`(0.5 g) / (cm^3) * (1 kg) / (10^3 g) * (10^6 cm^3)/(1 m^3)`

`(0.5 cancel(g))/(cancel(cm^3)) * (1 kg)/(10^3 cancel(g)) * (10^6 cancel(cm^3))/(1 m^3) = 0.5*10^3 (kg)/m^3 = 500 (kg)/m^3`

I hope this helps,
Steve