Which scientific law states the idea that elements combine in fixed ratios to form compounds?

The rule of stoichiometry.

Explanation:

The law, which was based on Dalton’s observations of the reactions of atmospheric gases, states that when elements form compounds, the proportions of the elements in those chemical compounds can be expressed in small whole number ratios.

Example, the reaction of the elements carbon and oxygen can result in the formation of both carbon monoxide (CO) and carbon dioxide (CO2). In CO2, the ratio of the amount of oxygen to the amount of carbon is a fixed ratio of 1:2, while in CO, the ratio is 1:1. In both the cases it is in the whole number as per the law and it has to be in the whole number for the integrity of the molecules which are present in the nature in their stable form.