How to manage task durations in half day increments?

We have many projects that have tasks are less than a day and the second half of the day’s task is dependent on the first days. The duration field doesn’t let us input partial days (ex: 0.5 or 1.5 days) so if we have two tasks on the same day, they show in conflict which impacts our ability to move items on the schedule and then have subsequent tasks be pushed “right” on the schedule on the timeline view.

Does any body know how to manage tasks with less than full day durations to manage a timeline schedule more granularly?

Correction: the second half of the day’s task is dependent on the first task earlier in the days.

We have our own duration field, a number field, where we write how many hours but could be days.