- Number of bacteria in one human being: 1 × 1014
- Number of humans on earth: 6 × 109
- Ergo, 'the' number is the average number of bacteria in humans multiplied by the number of humans.
So, have you ever asked yourself who Avogadro was? His full name first: Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto. He was born on 9 August 1776 in Turin into a noble family and died on 9 July 1856. He was perhaps not the most handsome man in Italy at the time. In 1811, he published Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons ("Essay on Determining the Relative Masses of the Elementary Molecules of Bodies and the Proportions by Which They Enter These Combinations"), which contains his famous theory.
In 1820, he became professor of physics at the University of Turin. For all his aristocratic upbringing, he turned revolutionary, which caused him to get fired from the chair. The dismissal was elegant, as the university officially declared: "...that it was very glad to allow this interesting scientist to take a rest from heavy teaching duties, in order to be able to give better attention to his researches." Deans, take heed. In 1833, he got his chair back and continued to do research on physics and quantitative measurements on molecules.
At the time he published his theory, it got scant attention. It went through a few gyrations, to be finally accepted in 1860 when his fellow countryman, Stanislao Cannizzaro (of the Canizzaro reaction fame), laid the matter to rest. The actual number was determined in a number of ways but the main credit goes to Jean Baptiste Perrin who got the Nobel Prize in Physics in 1926, in part for this contribution. He also coined the term 'Avogadro's Number'.
Now you have it, a modern way to determine the value of Avogadro's Number is simply to count the number of bacteria in one human and multiply that by the number of humans on Earth.