Quote from onlineacademiccommunity.uvic.ca/myuviclife/2016/06/07/homeopathy-put-into-perspective/
Homeopathic remedies are typically diluted so excessively that NO molecules of the original substance are present in the actual remedy. Essentially, this means that if you purchase a homeopathic remedy from the drugstore, you will be buying nothing but pills of lactic acid and water, which makes it no different from placebos used in drug trials. I encourage you to watch CBC’s Marketplace special on homeopathy, where they demonstrate that even the most sophisticated analytical instruments can’t detect any medicine in a homeopathic pill. What they did detect in the pills, though, was sugar.
These remedies can range in dilutions from 1 molecule of substance in 1,000,000,000,000,000,000,000,000,000,000 molecules of water, and can even go up to a 1/10^400 dilution, which is one molecule of substance for every 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 molecules of water. That’s what I call dilute.
It’s tough to get an appreciation for how large of a number this is unless it’s made a little easier, so I did some number crunching to give this analogy.
1/10^400 is equivalent to taking one grain of rice, crushing to a powder and dissolving it in a sphere of water the size of the Solar System, with the Sun at the center and the orbit of Pluto at the outside (giving this sphere a radius of 3.67 billion miles), and then repeating that process 8 more times in a series. Now, if that isn’t dilute, I don’t know what is.