What is the pH of a 0.066 M solution of HCl?

0.066M has two significant digits, therefore, the answer will have two significant digits. When taking the log of a number the precision of the original number is reflected in the numbers to the right of the decimal. (The number to the left of the decimal comes from an exponent.)

HCl is a strong acid and ionizes completely. Therefore, [H+] = 0.066M

pH = -log[H+]
pH = -log(0.066)
pH = 1.18 ................ to two significant digits

1 mole of HCl completely dissociates to give 1 mole of H₃O⁺ ions.
Concentration of HCl before dissociation = 0.066 M
In the solution, [H₃O⁺] = 0.066 M

pH = -log[H₃O⁺] = -log(0.066) = 1.2