# 6.03 Resolution

Increasing the number of digits on the display to four would enable it to display values such as 100.1, 100.2 etc . This would give an improved resolution of 0.1cm and reduce the uncertainty to 0.05cm. However, the same problem still exists when it comes to values such as 100.01cm 100.02 cm. The resolution could be improved further by adding more digits. This would reduce uncertainty further leading to increased precision. However no matter how many digits are added there will always be a limit to the resolution of the display which will produce some uncertainty in the measurement.

If instead of a digital display we placed a ruler with cm markings in the tank we would now be able to see the water level changing in between 100 and 101 cm meters. However we could not quantify any of the values in between 100 and 101 as there are no markings to read from*. So once again we would have limited resolution from our measuring instrument. (*In practice we could estimate accurately to within a half a centimetre division so we could in fact quantify 100.5, 101.0, 101.5 cm etc.) Using a ruler with a scale in millimetres would improve the resolution of the instrument. However there is a practical limit to placing the markings closer and closer together on a scale in order to improve the resolution. Soon we would have difficultly seeing the spaces between markings!

(Note It may seem that when the water level appears to lie dead one of the markings, say for instance the 100cm mark that we can have an exact reading. However a magnified image would illustrate that the 100cm marking itself has thickness so covers a small range of values which again produces some uncertainty.)