Saving to LAS file using laspy, correctly

I have a text file, each line in the text file has X,Y and Z coordinates eg:

551124.5841823021 470778.1953796738 318.1167521614109

I want to read the data and export it to LAS format, by using laspy.
The code I use, inspired from :

header = laspy.header.Header()

with open(input_file, "r") as file:
     lines = list(line for line in (l.strip() for l in file) if line)
output_X = []
output_Y = []
output_Z = []
for line in lines:
    splited = line.split()
    output_X.append(float((splited[0])))
    output_Y.append(float((splited[1])))
    output_Z.append(float((splited[2])))
output_file = input_file.rsplit(".", 1)[0]+"_changed.las"
outfile = laspy.file.File(r"{}".format(output_file),
                          mode="w", header=header)

outfile.X = numpy.array(output_X)
outfile.Y = numpy.array(output_Y)
outfile.Z = numpy.array(output_Z)

outfile.close()

The values I expect to find should be of the same type as those from txt file, however, if I read the file I get:

[((551124, 470778, 318, 0, 0, 0, 0, 0, 0),)
((551124, 470779, 318, 0, 0, 0, 0, 0, 0),)
((551124, 470780, 318, 0, 0, 0, 0, 0, 0),) …
((551438, 470707, 315, 0, 0, 0, 0, 0, 0),)
((551438, 470708, 315, 0, 0, 0, 0, 0, 0),)
((551438, 470709, 315, 0, 0, 0, 0, 0, 0),)]

I want the entries to be of type float, with decimal. I know it should be possible, since I have LAS files received from a third party, that have decimals.
Should I be setting the scale for the LAS file on export?
Also, if I open the output file in a software that reads LAS files, ArcGIS, points are not represented.
What am I doing wrong?