Part-hours

The gaps that are not whole hours

Not every gap is a whole number. The ones that are not are the ones people get wrong.

Part five

8 notes in this part

Seventy-two offsets here are not whole numbers of hours, and forty-eight of them leave shared time. They get left out of every conversation.

Reference

Twenty-four offsets are half hours and sixteen leave something. The law is unchanged; what changes is that nothing starts on the hour.

Reference

Forty-eight offsets sit at a quarter or three quarters of an hour. They are the only place the answer stops being a round figure.

Reference

A fractional answer is not an invitation to round. Rounding down discards time that exists; rounding up spends time that does not.

Analysis

Forty-eight of the seventy-two part-hour offsets leave shared time: thirty-two at quarter marks and sixteen at half marks.

Reference

The shared stretch no longer starts on the hour, and everything built on hourly slots loses a slot. The loss exceeds the offset that caused it.

Analysis

The one-hour-per-hour rule is exact for any offset, whole or not, while both working days are the same length. The proof never mentioned integers.

Reference

Part-hour offsets are omitted from almost every discussion of these arrangements. The reason is not a good one, and the cost falls on one side.

Analysis