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 kilogrammeter3kilogrammeter3 and the density of silicon in other units: 2.332.33 gramcentimeter3gramcentimeter3. You decide to convert the density of silicon into units of kilogrammeter3kilogrammeter3 to perform the comparison. By which combination of conversion factors will you multiply 2.332.33 gramcentimeter3gramcentimeter3 to perform the unit conversion?

The conversion factors you will use to multiply is 1/0.001 or simply 1000 to perform the unit conversion.

Explanation:

To convert from gram/centimeter³ to kilogram/meter³

First,

NOTE:

1 kilogram = 1000 gram, that is 1 gram = 0.001 kilogram; and

1 meter = 100 centimeter, that is 1 centimeter = 0.01 meter

then,

1 meter³ = 1000000 centimeter³, that is

1 centimeter³ = 0.000001 meter³

Now, we can write that

1 kilogram/meter³ = 1000 gram / 1000000 centimeter³

= 0.001 gram/centimeter³

If 1 kilogram/meter³ = 0.001 gram/centimeter³

Then, 1 gram/centimeter³ = 1/0.001 kilogram/meter³  = 1000 kilogram/meter³

Hence, 1 gram/centimeter³  = 1000 kilogram/meter³

∴The conversion factors you will use to multiply is 1/0.001 or simply 1000 to perform the unit conversion.

That is,

2.33 gram/centimeter³ will be 2.33 × 1000 kilogram/meter³

= 2330 kilogram/meter³