What does it mean that a multimeter is four and a half digit?
At most ranges, the smallest reading is 1/19,999 of the maximum (e.g. on the 20 volt range, values range from 2.000 to 19.999 in steps of 0.001). Although it may seem odd to regard a meter that can read up to 19,999 as being a full "half digit" better than one which can read up to 9,999, common terminology for many decades has been to use the term "1/2 digit" to mean a leading digit that's zero [blank] or one, "2/3 digit" to mean 0, 1, or 2, and "3/4 digit" to mean 0, 1, 2, or 3. The fraction is explained thus: the numerator is the maximum display value for the MSB - '1' or '1/2', '3' for '3/4'; the denominator is the total number of possible display values '0, 1' (hence '2' for '1/2'), '0, 1, 2, 3' (hence '4' for '3/4'). Thus, "3 3/4 digit" doesn't mean that the numerical significance is 3.75 times as much as much as for a 1-digit meter, but instead that there are three full digits, plus a digit that shows a value 0-3.
Source: What's a half digit anyway?
The final answer given in not completely representative of what will be found on a meter. A small correction to the description is needed.
The '19,999' really means 20,000: 4 digits for the 0,000 and an implied 1. Because it is implied it is give 9,999 but really means 10,000:1 of the full scale value. That is the missing bit.
If the scale is 0-5 volts, then the reporting display show 0-5 volts divided by 10,000 for 4 digits, and 20,000 for 4.5 digits. In other words the extra 'half digit' means it can display a change of 1/2 the amount indicated by a 4 digit machine.
If it was a 0-10,000 volt meter, it can show 1 volt steps with 4 digits (really only going up to 9,999 volts).
An extra half digit means it can show 0.5 to 9,999.5 volts, but not 9,999.2 or 9,999.8. The last digit is either 0 or 5. That is the '1/2'.
A 5-digit machine could display 9,999.1 and 9,999.7 and 9,999.5. That is a 'full 5 digits'.
Some scales show 0.2 g resolution, not 0.1 so they can show 999.2, 999.4, 999.6, 999.8 and 999.0.
How many digits is that? :)
That means that the maximum reading on the display is 19999 - the first digit can only be 0 or 1.