.LOW_RESOLUTION_TIME

[ali hagigat]

I copied some lines of the manual, page 33:
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.LOW_RESOLUTION_TIME: dst
dst: src
cp -p src dst

Since ‘cp -p’ discards the subsecond part of ‘src’’s time stamp, ‘dst’
is typically slightly older than ‘src’ even when it is up to date.
The .LOW_RESOLUTION_TIME line causes make to consider ‘dst’ to be up
to date if its time stamp is at
the start of the same second that ‘src’’s time stamp is in.
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When we used -p , it means preserve time-stamp, so how ‘dst’ is
typically slightly older than ‘src’ ? The time-stamp of both files are
exactly the same!!
And concerning the last statement:
if the time stamp of 'dst' is at the start of the same second that
‘src’’s time stamp is in, so the both time-stamps are the same and
'dst' is up-to-date, why we need  .LOW_RESOLUTION_TIME to say that
'dst' is up-to-date?
Without using .LOW_RESOLUTION_TIME, the time stamp of both files seems
to be the same and 'dst' seems up-to-date already.