What is the numerical value in a meters per second squared of the acceleration of an object experiencing a true free fall?

The acceleration of an object by gravity depends on where the object is. The AVERAGE acceleration of gravity on the Earth is 9.81 m/s². Effective gravity on the Earth's surface varies by around 0.7%, from 9.7639 m/s2 on the Nevado Huascarán mountain in Peru to 9.8337 m/s2 at the surface of the Arctic Ocean.

Of course if you drop an object on other bodies - such as the moon or Mars, the acceleration is MUCH different that it is on Earth.