"A total of 0.0606 moles of NaOH was" or "were"?

When referring to amounts of objects as opposed to the objects themselves, you normally use singular agreement. This has nothing to do with fractional amounts, and nothing to do with the use of 'a total of', but is a property of amounts in general.

• 40 litres of water was/*were poured into the tank.
• (A total of) 0.0605 moles (3 s.f.) of NaOH was/*were originally added to the aspirin.

We can see this when use anaphora to refer to the amount.

• 40 litres of water was poured into the tank. It/*They filled it to the brim.
• John weighs 200lbs. It is too much for his height./*They are too much for his height.

As TimLymington points out in the comments, there are some interesting wrinkles in this, although they simply confirm the statement above. Fractions always control plural number within the noun phrase, but whether that noun phrase will control plural verbal agreement depends on whether it refers to a measure or the objects themselves. So in the example below, plural agreement is used (not singular) because the noun phrase "0.5 apples" refers to actual apples and not to a measure.

• 0.5 apples were added to the mixture.

We can see this more clearly with the following examples, which don't use fractions.

• 30 lbs of potatoes were/?was peeled for the banquet.
• 30 lbs of potatoes is/*are not enough to feed this crowd.

In the first example, we are referring to the actual potatoes, and so the agreement is plural. Singular is marginally possible if we are referring to the measure. In the second example we are referring to the measure, and agreement is singular.

In case any other scientist consults this page he should be reminded that according to the standard SI units of nomenclature, which all reputable modern scientific journals follow:

1. Units are not written in full, but abbreviated.

2. Unit symbols are unaltered in the plural

Thus, the English Scientific Usage is:

A total of 0.0605 mol of NaOH was originally added to the aspirin

and

A total of 6.05 mol of NaOH was originally added to the aspirin

(The abbreviation for ‘mole’ being ‘mol’)

As explained in the accepted answer, the verb is in the singular in any case.

Examples are not easy to find just by surfing because of the scientific style of writing in the passive and naming the constituent with the amount following in parentheses, but here is one from the respected US journal, Biochemistry (vol 14, p.4828, 1975):

“To 0.6 ml of vesicle solution was added 0.2 ml of 1.6% Triton…”

(‘ml’ is the abbreviation for ‘millilitre’)