INR is a normalized ratio (International Normalized Ratio). The ratio has to do with the thrombin level of the reagent -- it's the thrombin (the reagent) that effects the prothrombin time. In the labs, reagents with a specific value are used for testing, and it's the prothrombin time divided by this standard, specific value, that provides the INR.
Meters do this in a similar way. The CoaguChek S uses a code chip - the chip provides the denominator for the INR (this is the value of the rabbit brain thrombin in the reagent on that batch of strips). The ProTime meters have the denominator and other information coded directly on to the 'strips' (which they call cuvettes). The ProTime cuvettes have the reagent value and an expiration date coded onto them - so when the test is run, the correct value is determined - and if the strips have expired, the meter won't accept them.
The InRatio strips come with a batch number. When a test is run on the InRatio, the meter asks if the number on the strip is the same one as the number stored in the meter. Presumably, this batch number also contains the correct value for the reagent, so the results are accurate. Your InRatio meter SEEMS TO BE dividing by ten and rounding - but it's actually applying the reagent value to the determination - in this case, it's somewhere around 10. It may also be adjusting for temperature, which makes it a bit less than predictable if you divide the prothrombin time by the INR value for many tests.
So - for ANY test - lab or handheld meter - the value of the reagent is a critical factor in determining the INR.
Prothrombin time DOES vary based on the value of the reagent, so it's not a valuable number. It is possible that the ambient temperature may also be a factor - blood may clot more quickly at a higher temperature than at a lower one - but I'm not entirely sure if this is actually accounted for by the meters (which heat the strips before testing). The NORMALIZED Ratio is the one to look for.
(I've used three types of meters - each with different reagent values. The prothrombin times for tests made with the CoaguChek S were always nearly twice that for the ProTime meters. The Prothrombin times for the InRatio meters were always pretty close to those for the ProTime meters. The prothrombin times weren't useful diagnostically -- it was the coding/reagent values that were significant, and the reagents in each system had slightly different values)