Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The ordinal number matching the number decillion in a series.
 n. One of a decillion equal parts.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. The ordinal form of the number decillion
 n. The person or thing in the decillionth position.
 n. One of a decillion equal parts of a whole.
from the GNU version of the Collaborative International Dictionary of English
 adj. Pertaining to a decillion, or to the quotient of unity divided by a decillion.
 n. The quotient of unity divided by a decillion.
 n. One of a decillion equal parts.
from The Century Dictionary and Cyclopedia
 Pertaining to a decillion; having the magnitude or position of one of a decillion equal parts.
 n. The quotient of unity divided by a decillion; one of a decillion equal parts.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Hahnemann tells us that a single dose of the 30th dilution of Aconite, which contains but the decillionth of a drop of the tincture of the remedy, will cure acute pleurisy in twentyfour hours.

But for persons of very delicate nerves it is proper that the dilution should be carried to the decillionth degree.

Yet this is given only at the quadrillionth, or fourth degree of potency, and various substances are frequently administered at the decillionth or tenth degree, and occasionally at still higher attenuations with professed medicinal results.

There are those whose minds are satisfied with the decillionth dilution of a scientific proof.

"To be called on to believe that the decillionth of a grain of charcoal or oystershell, is capable of producing hundreds of the most formidable symptom, and of curing, as if ny magic, the most inveterate diseases  while we can take ounces, nay pounds, of the same substance into our stomachs with no other inconvenience than its mechanical bulk  seemss so gratuitous an outrage to human reason that the mind instinctively recoils from the propositio."

"fractions of the sextillionth or decillionth degree."

Simplified down to kindergarten level, say the difference between A and B is, maybe, onedecillionth of the difference between X and A, and the difference between B and C is onedecillionth of the difference between X and B, and so on  "
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