The density of a substance is \(5 \mathrm{~kg}\) per litre. Express it in \(\mathrm{g} \mathrm{cm}^{-3}\).

Understanding the concept of mass unit conversion is crucial for many scientific calculations, including those involving density. Mass can be measured in units like grams (g), kilograms (kg), pounds (lb), and tons, among others. For this exercise, we focus on converting kilograms to grams.

To perform a mass unit conversion from kilograms to grams, we use the conversion factor where 1 kilogram is equivalent to 1000 grams. This means to convert a mass value from kilograms to grams, you simply multiply it by 1000.

Example: To convert 5 kg to grams, the calculation would be:
5 kg \( \times \) 1000 g/kg = 5000 g

It's important to remember that multiplying by the conversion factor changes the unit but not the actual mass of the object. Consistent use of units throughout a problem is essential to obtaining correct results.

In parallel with mass, volume unit conversion is another vital process required in many areas of science and engineering. Volume can be measured in liters (L), cubic meters (m³), cubic centimeters (cm³), and more. Specifically, when dealing with smaller quantities in the laboratory or in calculations such as density, converting liters to cubic centimeters is often necessary.

The conversion factor between liters and cubic centimeters is that 1 liter is equal to 1000 cubic centimeters. This is derived from the metric system where 1 cm³ is defined as the volume of a cube that is 1 cm on each side. Therefore, to convert from liters to cubic centimeters, multiply by 1000.

Example: To convert 1 liter to cubic centimeters:
1 L \( \times \) 1000 cm³/L = 1000 cm³

When performing volume conversions, it’s key to use the correct conversion factor to ensure that your volume measurement is accurate.

Finally, the concept of density calculation ties together the understanding of mass and volume conversions. Density is defined as the mass per unit volume of a substance and is expressed with various units, such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).

For a density calculation, you divide the mass of the substance by its volume:
\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]
Completing this exercise, where the mass is 5000 g (after converting 5 kg) and the volume is 1000 cm³ (after converting 1 L), the density calculation becomes:
\[\text{Density} = \frac{5000 \text{ g}}{1000 \text{ cm}^3}\]
Therefore, the density is 5 g/cm³. This value indicates that within each cubic centimeter of the substance, there’s a mass of 5 grams. This is a fundamental property used to characterize substances and has many practical applications in science and industry.