For the unfamiliar, a "board foot" is a unit of lumber volume representing a square foot of board with 1 inch thickness. So an 8' long board 12" wide and 1" thick is 8 board feet. Or half as wide and twice as thick (6" x 2") in the same length is also 8 board feet. You get the idea.
When you say one inch wide, do you mean one of the twelve things in a foot, or one of the two things in the width of a 2x4?
So in a 10ft long 2x4 it would be the actual size of a 2x4 (1.5"x3.5"x10').
A standard board foot would be (1"x12"x12"), or any other math that makes up the same volume.