In this question, you are given three pressures ... in three different units and you have to compare them to determine the greatest, middlest, and smallest pressure value.
Get a Game Plan
Like any problem in Chemistry, it is important to have a Game Plan. A good game plan equips you with a strategy for proceeding from the given information in the problem to the destination - the answer to the problem.
There are probably two basic game plans that a student could use to answer this question. The first Game Plan is to treat the question like a conversion problem. Select a unit - like atmospheres - and convert the two non-atm amounts to atmospheres. That is convert the pressure value in psi to atm and the pressure value in mm Hg to atm. Using this Game Plan, you would have to use the unit equivalencies (1 atm = 14.7 psi AND 1 atm = 760 mm Hg) to make two conversion factors and convert to Pressure in atm units. Once all three Pressure amounts are in atm units, you can easily compare to determine which is greatest, middlest, and smallest.
The second Game Plan (the one we are strong advocates of) is much more conceptual in nature. It involves head math and some thinking. This Game Plan begins by conceptualizing the size of an atm to that of a psi to that of a mm Hg. Since approximately 15 psi units are equivalent to 1 atm unit, a single psi unit must be rather small compared to a single atm unit. In fact, a psi is roughly 1/15-th of an atmosphere. Similarly, a mm Hg unit is smaller still - about 1/760-th of an atm. So if you have one of each of these units, then your 1 atm pressure is considerably large compared to the other pressures and your 1 mm Hg is considerably small compared to the other pressures.
