Show that for 1 kg of pure gold the volume of water displaced is 51.8 cm^3

I know that the density of pure gold is 19.32 gm/cm^3 so 1 kg/19.32 gm/cm^3= 0.05175 ?

I have come along way with this problem and feel like I am close, but now I need help.
How do I get kg and gm to cancel?
How do I get this to be 51.8cm^3?

1 kg = 1,000 grams

so
1,000 grams (1 cm^3/19.32 grams) = 51.8 cm^3

always multiply by a ratio that is the same top and bottom but in different units so that the units cancel
for example if I were given this the other way as 51.8 cm^3 of gold, then
51.8 cm^3 (19.32 grams/1cm^3) = 1000 grams because the cm^3 cancels top and bottom and we are left with grams.

chicken

To solve this problem, we will use the relationship between mass, density, and volume:

Density = Mass / Volume

Since you want to find the volume of water displaced, we need to rearrange the formula:

Volume = Mass / Density

First, we need to convert the density of pure gold from grams per cubic centimeter (gm/cm^3) to kilograms per cubic centimeter (kg/cm^3):

Density of pure gold = 19.32 gm/cm^3

To convert to kg/cm^3, we need to convert grams to kilograms:

1 kg = 1000 gm

So, the density of pure gold in kg/cm^3 is:

Density of pure gold = 19.32 gm/cm^3 * (1 kg / 1000 gm) = 0.01932 kg/cm^3

Now we can find the volume of water displaced using the given mass of 1 kg:

Volume = 1 kg / 0.01932 kg/cm^3

Volume = 51.77 cm^3 (rounded to two decimal places)

Therefore, the volume of water displaced by 1 kg of pure gold is approximately 51.77 cm^3.

To solve this problem, we need to convert the density of gold from gram per cubic centimeter (gm/cm^3) to kilogram per cubic centimeter (kg/cm^3).

Step 1: Convert the density of gold from gm/cm^3 to kg/cm^3
Since 1 kg = 1000 gm, we can divide the density of gold (19.32 gm/cm^3) by 1000 to convert it to kg/cm^3.

19.32 gm/cm^3 / 1000 gm = 0.01932 kg/cm^3

Now, we have the density of gold in kg/cm^3.

Step 2: Calculate the volume of water displaced
To calculate the volume of water displaced by 1 kg of gold, we can use the formula:

Volume = Mass / Density

Given that the mass of gold is 1 kg and the density of gold is 0.01932 kg/cm^3, we can substitute these values into the formula.

Volume = 1 kg / 0.01932 kg/cm^3
= 51.7364 cm^3

Step 3: Round the final answer to the appropriate number of significant figures
Since the given value is stated as 51.8 cm^3, we can round the final answer to match this value.

Therefore, for 1 kg of pure gold, the volume of water displaced is approximately 51.8 cm^3.