The progress of the reaction:
h2(g)+br2(g)↔2hbr(g)
can be monitored visually by following changes in the color of the reaction mixture (br2 is reddish-brown, and h2 and hbr are colorless).
a gas mixture is prepared at 700 k, in which 0.40 atm is the initial partial pressure of both h2 and br2 and 0.90 atm is the initial partial pressure of hbr. the color of this mixture then fades as the reaction progresses toward equilibrium.
give a condition that must be satisfied by the equilibrium constant k (for example, it must be greater than or smaller than a given number).

The Equilibrium constant K is far greater than 1; K>>1

Explanation:

The equilibrium constant, K, for any given reaction at equilibrium, is defined as the ratio of the concentration of the products raised to their stoichiometric coefficients divided by the concentration of reactants raised to their stoichiometric coefficients.

It tells us more about how how bigger or smaller the concentration of products is to that of the reactants when a reaction attains equilibrium. From the given data, as the color of the reactant mixture (Br2 is reddish-brown, and H2 is colourless) fades, more of the colorless product (HBr is colorless) is being formed as the reaction approaches equilibrium. This indicates yhat the concentration of products becomes relatively higher than that of the reactants as the reaction progresses towards equilibrium, the equilibrium constant K, must be greater than 1 therefore.

i do not get it   at all

there are two significant figures.