Show somebody to something
If this is from Whitman's poem, Song of Myself, the full clause in question is
They ... show me to a cent,
Exactly the value of one and exactly the value of two, and which is ahead
Here "to a cent" is telling how accuately they showed him the the value of things. The direct object (the thing being showed) is "the value of one and ... the value of two". The indirect object (the person seeing the thing being showed) is the narrator.
It means he wasn't shown the value very crudely (i.e. to the nearest dollar, for example), but very accurately, with less than a penny of uncertainty as to the value.
Some similar usages:
Mr. Moneybags knew the value of his company to the dollar.
The carpenter measured the length of the wall to the inch.
This is definition 5 of to at Meriam-Webster.com
- used as a function word (1) to indicate the extent or degree (as of completeness or accuracy)...
Show is a bitransitive verb. It isn't that it needs a preposition, exactly; the problem is that it has two objects. One is a person, an experiencer, the audience; and the other is what's being shown to the audience, the show. Prepositions are useful to mark them. For instance, the following two sentences are both grammatical, and both mean the same thing:
- He showed her the car.
- He showed the car to her.
Which one to use is up to the speaker, who may prefer either order of objects, or might like one extra, or one fewer, syllables.
There is another idiom with show and to, however, which is merely transitive; it means to guide a person (typically a guest) to a particular location. It takes a personal noun phrase as object and a prepositional phrase with to and a locational noun phrase.
- He showed her to the Observatory.
- He showed her to the car.
The last sentence means that he guided her (in person) to the location of the car.