Question Video: Converting Density Units

The density of gold is 19,320 kg/m³. What is this value in grams per cubic centimeter?

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Video Transcript

The density of gold is 19,320 kilograms per cubic meter. What is this value in grams per cubic centimeter?

In order to answer this question, we need to work out how we can convert from kilograms per cubic meter to grams per cubic centimeter. We know that there are 1,000 grams in one kilogram. This means that in order to convert from kilograms to grams, we need to multiply by 1,000. There are 100 centimeters in one meter. In this question, we are dealing with cubic meters, the units of volume. Cubing 100 gives us one million. Therefore, there are one million cubic centimeters in one cubic meter. This means that to convert from cubic meters to cubic centimeters, we multiply by one million.

We can use this information to work out how we would convert from kilograms per meter cubed to grams per centimeter cubed. We need to multiply the numerator by 1,000 and the denominator by one million. Let’s consider the fraction 1,000 over one million. We can divide the numerator and denominator by 1,000, which gives us one over 1,000. This means that to convert from kilograms per meter cubed to grams per centimeter cubed, we need to multiply by one one thousandth. This is the same as dividing by 1,000.

We need to divide 19,320 by 1,000. Dividing by 1,000 moves all of our digits three places to the right. This means that the density of 19,320 kilograms per cubic meter is the same as 19.32 grams per cubic centimeter. The density of gold in grams per cubic centimeter is 19.32.

To convert between the two different units of density, we can divide or multiply by 1,000. To go from kilograms per cubic meter to grams per cubic centimeter, we divide by 1,000. And to go the other way, we multiply by 1,000.

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