Question

You would like to know whether silicon will float in mercury and you know that can determine this based on their densities. unfortunately, you have the density of mercury in units of kilogrammeter3 and the density of silicon in other units: 2.33 gramcentimeter3. you decide to convert the density of silicon into units of kilogrammeter3 to perform the comparison. by which combination of conversion factors will you multiply 2.33 gramcentimeter3 to perform the unit conversion?

Answer 1

The answer is 1000

Density formula is weight/volume, so the unit should be gram/centimeter^3. To  convert gram/centimeter^3 into kilogram/meter^3, the conversion factors would be:
(gram/centimeter^3) / (kilogram/meter^3)
= (gram/kilogram) /(centimeter^3/meter^3)
= (gram/ 1000gram) / (centimeter^3/ 100^3 centimeter^3)
= (1/1000) / (1 / 100^3)
= 1,000,000/1000= 1,000

Answer 2

Answer : 1000

Explanation : We know the aim that we have to compare the densities of both the material which is silicon and mercury. The only difficulty is in the units; as they have been expressed in different terms.

Ideally density is measured in  kilogram per cubic meter $(kg/m^{3})$

And we need to convert it to gram per cubic centimeter  $(g/cm^{3})$

We need to simply take the ratio of both the units and find the conversion factor for the same.

∴ $(g/cm^{3})$ / $(kg/m^{3})$

Here we can compare gram ⇒ kilogram is 1000; ∴ 1 kilo gram = 1000 g

and centimeter ⇒ meter is also 100 and ∴ 1 meter = 100 centimeter

Now, applying these conversion values in the above expression we get;

= $(g / 1000 g) / (cm^{3}/ 100^{3} cm^{3})$

Which comes to

= $(1/1000) / (1 /100^{3})$

And finally we get the answer as

= (1,000,000) / (1000)

Which is = 1,000

Therefore, the answer is 1000.