**Hint:** Data doesn't obey Law of Definite Proportions. Mass ratios of dinitrogen and dioxygen vary. Identify patterns in data and use chemical formula multiples.

**Solution:**

**(a) Law of Multiple Proportions:**

When the mass of dinitrogen is 28 g, the masses of dioxygen combined are 32 g, 64 g, 32 g, and 80 g. The corresponding ratio is 1:2:1:5. This forms a simple whole-number ratio, illustrating the law of multiple proportions. The law states that "if two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers."

**(b) Metric Conversions:**

(i) To convert 1 km to mm, we use the fact that 1 km is equal to 1,000 meters, and 1 meter is equal to 100 centimeters, and 1 centimeter is equal to 10 millimeters.

Therefore, 1 km = 1,000 m × 100 cm × 10 mm = 1,000,000 mm.

Additionally, we can convert from meters to picometers using the fact that 1 meter is equal to 10^12 picometers.

So, 1 km = 1,000,000 mm = 10^12 pm.

(ii) To convert 1 mg to kg, we use the fact that 1 milligram is equal to 0.001 kilograms, and to convert from milligrams to nanograms, we can use the fact that 1 milligram is equal to 10^6 nanograms.

Therefore, 1 mg = 0.001 kg = 10^6 ng.

(iii) To convert 1 mL to liters, we use the fact that 1 milliliter is equal to 0.001 liters, and to convert from milliliters to cubic decimeters (dm^3), we use the fact that 1 liter is equal to 1 dm^3.

Therefore, 1 mL = 0.001 L = 0.001 dm^3.

**Note:** The law of multiple proportions is a fundamental concept in chemistry, and it demonstrates how elements can combine in different ratios to form distinct compounds. Understanding metric conversions is essential for working with units of length, mass, and volume in scientific calculations.