10 digits of accuracy
It's singular. If you go by strict rules about the number of the "head" of the phrase or the "simple subject" ("digits"), you'll conclude that it's plural, but in English we use a singular verb with a plural noun to indicate that the listener should understand a singular meaning. The meaning is what's important here, not just syntactic rules.
Some more examples will help clarify what's happening here.
Two days is all the time I can give you.
This means that the speaker is allowing the listener two days to complete some task (which is not stated); the speaker would like to allow more time, but waiting any longer than two days would cause a problem for the speaker. "Two days" is understood as a quantity which is the subject of the sentence. It would be wrong to say this:
Two days are all the time I can give you.
This doesn't make sense in English because it suggests thinking of the two-day interval as a collection of two separate intervals, each of which is all the time the speaker can give the listener. The intended meaning is that the "two days" are to be understood as a single interval of time. The singular verb confirms this interpretation.
A dozen hamburgers is not what I ordered.
Hamburgers is not what I ordered.
because the speaker wants the listener to understand that he is referring to a single order. But:
A dozen hamburgers are in the bag.
Some hamburgers are in the bag.
because the speaker wants the listener to think of the hamburgers as multiple, distinct things.
In engineering, three digits is enough for most practical calculations.
10 digits of accuracy is required.
are correct because when making calculations, you don't think of the degree of accuracy as something that can be divided into separate digits. For example, you couldn't do one calculation with seven digits of accuracy, and another calculation with three digits of accuracy, and combine them to get ten digits of accuracy. The degree of accuracy is an attribute of the result of a calculation. It's only one thing, not many things.
If you like, you could say that the subject of the sentence is the phrase "10 digits of accuracy" as a whole; and as a whole, the phrase is singular even though "digits" is plural. It's not unusual in English for phrases to work grammatically in a way that's very different from the words they contain.
If you omit "of", then you must make a compound adjective with a hyphen and convert "digits" to the singular:
10-digit accuracy is required.
This is a common pattern in English. Here are a few more examples:
A three-alarm fire. [Not
For $190, you get a haircut, a manicure, a pedicure, and a half-hour tanning session.
Don't use a five-dollar word where a fifty-cent word will do.
There are a few exceptions, though, established by long usage and old precedents, such as:
The name The Hundred Years’ War has been used by historians since the beginning of the nineteenth century to describe the long conflict that pitted the kings and kingdoms of France and England against each other from 1337 to 1453.
Notice the apostrophe, indicating that Years' is possessive.