Verbs – Should Plural Verb be Used for a Fraction?

The fraction is considered a singular quantity in this particular sentence, just as the plural 20 ml in "Twenty milliliters of reagent was added to the culture medium" and the plural US$5 in "Five American dollars is a lot to pay for something like that". Ergo, "Nine tenths of the pillar has rotted away" is correct.

Here's what one grammar "expert" says:

Rule 9
"With words that indicate portions—percent, fraction, part, majority, some, all, none, remainder, and so forth —look at the noun in your of phrase (object of the preposition) to determine whether to use a singular or plural verb. If the object of the preposition is singular, use a singular verb. If the object of the preposition is plural, use a plural verb.

Examples:

Fifty percent of the pie has disappeared.
Pie is the object of the preposition of.
Fifty percent of the pies have disappeared.
Pies is the object of the preposition.
One-third of the city is unemployed.
One-third of the people are unemployed."

[My emphasis. "City" is singular, as is "pillar"; "people" is plural, but "pillar" is not: it would be were it "pillars", but that ain't the case.]

Another "authority" says this:

Fractions and percentages

Fractions and percentages take the singular when they modify a mass noun and the plural when they modify a plural noun; either the singular or the plural may be used when they modify a collective noun.

Fifty percent [Can be replaced by nine-tenths] of those children have psychological problems.

One-half [Can be replaced by nine-tenths] of the cake has been eaten." [Italicized words in square brackets are my editorial additions.]

This kind of structure is one of those hotly contested usages that twist the brow and carpals as they twist the subarachnoid cerebellar noodles as if they were merely British knickers or American panties. I recommend a cold shower for anyone who suffers from this fractional syndrome.