"Uncertainty" is an ambiguous term. For a standard measurement in physics, there are two recognized components of error.
Accuracy is a measure of how close a measurement matches the "known" value. Obviously, the known or true value of a measurement isn't normally known, but for situations such as determining the concentration of a chemical in a chemistry experiment, you would deliberately mix a known concentration of this chemical, known as the "standard", and make a measurement of this concentration to ensure that your measurement device/method was giving you a true reading.
Precision is a measure of how many significant figures you can assign to a given measurement, and is related to the device that was used to make the measurement. For a meter stick measurement, where the meter stick is marked in centimeters and contains no millimeter marks, you can measure lengths to the nearest centimeter and estimate the fraction of a centimeter that is exceeded by the unknown length. Thus, a line that is 65.3 centimeters long would be reported as being 0.653 meters in length, where the least significant digit (e.g., "3") is recognized as an estimated value. You wouldn't report the length as 0.6530 meters, because the rules of precision require that you only estimate and report the first estimated digit in your answer. Likewise, if a different meter stick was marked in centimeters and millimeters, you would report the measured line as 0.6532 meters, where again, the least significant digit (e.g., "2") is recognized as an estimated value. Note that if precision is properly reported, it is easy to discern that the first measurement was taken with a device that was marked in centimeters while the second measurement was taken with a device that was marked in millimeters.
Regarding the "uncertainty" in the measurements described above, BOTH measurements give an answer within the precision of the device that was used. EACH answer is valid "information" in the context of accuracy and precision. Whether one answer can be considered as "better" or more valid than the other often depends on how precise an answer you need for a given application or experiment. This, of course, means that there is no strictly defined relation between "uncertainty" and "information", as both of these terms are ambiguous within the context of established physics norms.