In my research on math books, I had been surprised by how recent it seemed that number lines had come into use in textbooks. Prior to this summer, my notes read, "I have not, at this point, seen a book (or article) prior to 1960 which illustrates a general number line with anything other than integers."
But over my summer road trip, I was able to move that date back considerably as a result of some documents I received from Dave Renfro. Although the term, "Number line" did not become common until around 1960, (it does appear as early as 1928) but the use of a number line with rational fractions appears in "A College Algebra" by Henry Burchard Fine in 1904,
and three years later, in 1907, there is an example of a number scale with an irrational (the square root of two) in Albert Harry Wheeler's "First Course in Algebra." I point out with some smugness that Mr. Wheeler is listed as the "Teacher of Mathematics in the English High School at Worcester, Massachusetts. Nice to have a first by a High School Teacher.
For more on my research on Math Books on the Number line The same page also has more general remarks about the development of math texts.