Both Uses

precise
in
Hatchet, by Gary Paulsen
(Edited)

He put an arrow to the string, pulled it back to his cheek, pointed it at a din hummock, and at that precise instant the bow wood exploded in his hands sending splinters and chips of wood into his face.
p. 118.2

precise = exact
There was garlic in it and some other spices and the smells came up to him and made him think of home, his mother cooking, the rich smells of the kitchen, and at that precise instant, with his mind full of home and the smell from the food filling him, the plane appeared.
p. 176.6 *

Definitions:

(1) (precise as in: about noon; 12:03 to be precise)
exact (accurate)

In the fields of science, engineering, and statistics, precise and accurate are not properly used as synonyms the way they are in general usage.

If you throw darts at a dartboard and keep missing the bullseye, but hit in the same place on the dartboard each time, you would be described as precise, but not accurate.

If you seldom hit the bullseye, but tended to get close each time, you would be described as accurate, but not precise.

Finally, if you hit the bullseye each time, you would be considered both accurate and precise.
(2) (precise as in: a precise personality)
meticulous (careful about details) -- especially to do things properly
(3) (meaning too rare to warrant focus)