When a reaction results in an almost complete conversion of reactants to products, chemists say that the reaction goes to completion?

Yes, that is completion reaction.
This type of reactions do not set up an equilibrium and goes until one of the reactants runs out.
Three major types of completion reactions are:
1. Formation of a slightly ionized product (for example mixture of sodium bromide and potassium chloride).
2. Formation of a gas (for example hydrogen gas from metal and acid).
3. Formation of a precipitate (feor example silver chloride).

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