Quick answer
When you book a single working day, choose Full day, Morning ½ or Afternoon ½. For a longer range you can start after lunch on the first day, or be back after lunch on the last. A half day counts as 0.5.
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Book a single half day
Open the Add leave form with the + button and set the same date for Starting and Ending. A How long? choice appears: pick Morning ½ or Afternoon ½. It takes 0.5 days from the allowance.
Half days within a longer break
For a range across several days, use the half-day options to start after lunch on the first day or be back after lunch on the last, so those days count as a half.
How half days show
A half day appears on the calendar and wallchart with an AM or PM tag, so it is clear at a glance which part of the day is booked.