1 psi equals to _______ atmospheric pressure.

Hint: There are certain systems for the measurement of physical quantities. This includes S.I. (Standard international) units, FPS (Foot pound second system), CGS (Centimeter gram second system), etc. These are named as per the base units taken for measurements. For example in FPS units the base unit for length is foot, that for mass is pound and that for time is second.

Complete answer:
We can easily convert the quantity from one system of units to the other system by establishing the relationship between the base units.
Now, the atmospheric pressure is the pressure which the molecules of air in our atmosphere exert on the surface of earth. Basically we can say that it is the pressure due to the weight of air molecules. It’s value is $1.013 \times 10^5 Pa$, where ‘Pa’ stands for pascal and is the S.I. unit of pressure.
Now, in the FPS system, the unit of pressure is ‘psi’ which stands for Pound force per square inch.
To convert it in S.I. unit, (in order to compare the two values) we know:
1 pound force = 4.44 N,
1 square inch = 0.000645 square meter [1 meter = 0.0254 inch]
Hence, let 1 psi = n Pascals
Or 1 pound force / sq inch. = n Newton / sq m
Or $1\times \dfrac{4.44}{0.000645 } \dfrac{Newton}{m^2} = n\ \dfrac{Newton}{m^2}$
Hence $n= 6890$
Which is our conversion factor. Hence 1 psi = 6890 Pa
Or $1\ Pa = \dfrac{1}{6890} psi$
Also from $1\ atm = 1.013 \times 10^5 Pa$
Or $1\ Pa = \dfrac{1}{1.013 \times 10^5} atm$
Hence equating the two as both represent 1 Pa:
$\dfrac{1}{6890} psi = \dfrac{1}{1.013\times 10^5} atm$
Or $1\ psi = \dfrac{6890}{1.013\times 10^5} \approx 6800 \times 10^{-5} atm = 0.068\ atm$
Hence we can say that 1 psi = 0.068 atmospheric pressure.

Note: For such types of conversion questions, it is advised to first let some relation between the unknown units of pressure and S.I. units and then find the conversion factor. Also, it is advised to work mainly with S.I. units as they are easy to work with.