Ammonia will decompose into nitrogen and hydrogen at high temperature. An industrial chemist studying this reaction fills a $200.mL$ flask with $2\mathrm{.}7$atm of ammonia gas, and when the mixture has come to equilibrium measures the amount of nitrogen gas to be $0\mathrm{.}14$atm.

Calculate the pressure equilibrium constant for the decomposition of ammonia at the final temperature of the mixture. Round your answer to $2$ significant digits.