In general, the accuracy tolerance conditions are a set of rules that which ever rule produces the highest tolerance, that rule identifies your tolerance. The easiest method I find understanding any accuracy information is to use some test numbers. I'll deal first with your first two conditions, for you provide enough information for a concise explanation. Lets say you were displaying a reading at 200. The +/- 1% tolerance rule states that your actual condition could be anything from 202 to 198 and still be considered accurate. The +/- 0.5 rule says that your tolerance range is 200.5 to 199.5. So your measurement with accuracy limits in this case is 200 +/- 2. Now if instead your display showed 30 then the 1% tolerance puts the range at 30.3 to 29.7. But the +/- 0.5 rule says that the range is 30.5 to 29.5. This means that your actual measurement and tolerance is now 30 +/- 0.5. Lastly the cryptic third digit rule. Likely your display does some auto-scaling that can be manually overridden. So your 200 reading could have been significant three digits of 200 or it could have been manually set to 020 * 10. In this form the third digit displayed will be in the tens place so this rule would put your 200 reading and tolerance at 200 +/ 10.

Lets say you were displaying a reading at 200. The +/- 1% tolerance rule states that your actual condition could be anything from 202 to 198 and still be considered accurate. The +/- 0.5 rule says that your tolerance range is 200.5 to 199.5.

Shouldn't it be 201.0 to 199.0?

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"Lets say you were displaying a reading at 200. The +/- 1% tolerance rule states that your actual condition could be anything from 202 to 198 and still be considered accurate."

So for the percentage tolerance conditional rule the tolerance is calculated from the reading presented such as, 200*1%*1/(100%)=2 for the tolerance.

200+2=202

200-2=198

"The +/- 0.5 rule says that your tolerance range is 200.5 to 199.5."

So this conditional rule states the tolerance is 0.5 for all cases regardless of the measurement.

200+0.5=200.5

200-0.5=199.5

Need I say more.

My mistake, I thought that it is the 0.5% rule. Humble, I ask for forgiveness!

In your question, it seems that the tolerances are additive. If they were one or another, it would have stated "whichever is greater" in the tolerance. Add all of the tolerances together in the same units (degrees C or degrees F).

Accuracy of 1% means that the reading will be within 1% of the standard reference method or absolutely correct value. +/-0.5 is the best resolution possible or the best precision possible (smallest tolerance). +/-3 digits I have no idea what it means. The key point is that +/-1% refers to ACCURACY (Calibration vs. standard) and +/-0.5 deg. to PRECISION (variation) around the relatively accurate reading. If you need an absolute accuracy (e.g. Thermodynamic work) you worry about +/-1%. If on the other hand, you only worry about your own process than you have only +/-0.5 deg. of Precission to worry about. It would be useful to know what you are using this instrument for and what may be the range of readings... Tolerance concept is not appropriate here.

Without the words "whichever is greater", The tolerances provided by the manufacturer are additive. If you are reading at 200°C and the resolution is 0.01°C for example, the tolerance would be ±1% of 200°C (2.0°C) + 0.5°C, + 3 digits (0.03°C). The tolerance at 200 degrees C in this example would be ±2.53°C with 0.01 °C resoultion.

You are technically correct that without the words "whichever is greater" added choosing the larger error is not precise. But there is a practical advantage to following this guide line. First, one is determining the likely or indistinguishable error tolerance band of a measurement not the absolute tolerance band. For the instrument is but one of the possible error sources in doing any measurement. In other words, citing this 2.53 tolerance, a reading of 200 will be likely actually be in the range of 202.53 to 197.47 at the instrument but not necessarily at the item being measured. So when one has a cumulative sum of errors, dropping the less significant error elements while not perfectly accurate is commonly done since one is attempting to quantify what cannot be known anyway.

However, I am certain that you are incorrect in your comment about 3 digits being 0.03. I'm certain this error is a factor of how many digits are displayed, not a fixed quantity. If it was a fixed quantity it would be added to the 0.5 fixed quantity error and become 0.53.

"In other words, citing this 2.53 tolerance, a reading of 200 will be likely actually be in the range of 202.53 to 197.47 at the instrument but not necessarily at the item being measured."

The question specifically refered to the display accuracy. This is not taking into account the sensor accuracy that would be root sum squared with the display accuracy for a system accuracy.

"However, I am certain that you are incorrect in your comment about 3 digits being 0.03. I'm certain this error is a factor of how many digits are displayed, not a fixed quantity. If it was a fixed quantity it would be added to the 0.5 fixed quantity error and become 0.53."

The reason for all three accuracy statments is this. With the % of reading spec, the unit will be less precise as the temperature increases. This must be. You can not expect a 2000 degree reading to be as precise as a reading at 0 degrees. % of reading allows for this. The second part of the accuracy spec is the 3 digits. As resolution decreases, the precision must also decrease. Thus the 3 digits part of the spec. We can not expect to be as precise with 1 degree of resolution as with 0.01 degree of resolution. 0.53 would be correct at 0.01 degree resolution. 0.8 would be the combination of the digits plus the half degree with 0.1 degree resolution. Instruments with this as part of their spec change resolution throughout the range. The half degree is mostly for some leway at zero since 2% of zero is zero.

Specmanship is a very interesting science all by itself. I have been a metrologist for NASA and a power company and the Air force. I have 30 years experience. I calibrate instruments with this type spec every day. We are probably talking about a Hart Scientific or Omega instrument. Either company could solve all of this confusion with one phone call.