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10^-3 and 10^3 serve as guidelines to determine whether a chemical equation strongly favors reactants or products. When the K value is between 10^-3 and 10^3, it just means that the equation does not favor reactants or products to such an extent that it is significant enough for people to acknowledge as one-sided.
When K is equal to 1 that means there is equal concentration of products and reactants. If K is larger than 1 that means the concentration of products is higher than the concentration of reactants so products are favored. If K is less than 1 that means the concentration of reactants is higher than the concentration of products so reactants are favored. Even though K might be between 10^-3 and 10^3 either the products or reactants are still favored because K is relative to 1. Lavelle just used 10^-3 and 10^3 as a reference because in acid and base equilibrium and ice tables when K is less than 10^-3 we dont need to use the quadratic.
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