The Decimals and display format dropdown control how values are displayed. If you tap the drop arrow on the display format box you get a scrollable list of display formats with examples of what they look like:

Engineering Notation ñ The point to this is the exponents are set to powers of 1000 which makes it easier to interpret than normalized scientific notation. This is similar to using commas between 1000s places because the number are thousands, millions, or thousandths, millionths, etc.
Time Formats ñ Time in Napier is held internally as a floating point number representing days and fractional days, e.g.Ý 3.5 is 3 days 12 hours, and .0034722 is 5 minutes. Dates are the number of days since the end of 1899, so Jan 1, 2001 Noon = 36892.5 (the number of days since the end of 1899).
The various time formats convert this type of value into something more useful. There is a choice between whether time should be shown as a time interval (days, hours, etc.) or a date. If the Gen Time format is selected, it looks at the value and for small values, selects an appropriate time interval, for very large values it selects date/time format.
Note that when entering a date, you must have a # sign before and after it so it is recognized as a date. The Date function allows selecting a date from a calendar and inserts it in the correct format. You can freely edit this, but keep to the same date/time format the Date function uses.
The time formats are actually functions that will return the number of days for that unit, e.g. Hours(12) = 0.5, because 12 hours is ‡ day, or .5.
Hexadecimal ñ Base 16 numbers which are sometimes used in computer applications. Hex numbers are signified by having &h before them, and & after, e.g. &h03A5&. Internally, Napier keeps all numbers including hex values as floating point. However, in hex format, the fractional part isnít displayed. It is still there though, so if you are in hex mode, &h0003& / &h0002& = &h0001&_, but if you continue with * &h0002&, the result will be &h0003&.
There is an integer divide operator \ in the Prog function dropdown that will truncate to just the integer value if that is what you want.
Often it is convenient to switch quickly between different display formats, so in addition to the full list ofÝ display formats in the Options dialog box, there is a button that cycles between the major display formats:

There are 4 values for the quick format button: num, sci, time, hex. As the button is tapped, it cycles through these values and the display format changes to match. The exact format selected, depends on the last settings in the Options dialog, both the overall format and decimal points displayed. For the num setting, it is always the numeric format, sci is either scientific or engineering depending on the last selection, time is the last selected time format, and hex is always hexadecimal.