Recall that measurement is the process of assigning an abstract mathematical object to some property of the physical world. In our example, we assign a number to the length of the spring in the experiment by reading a number from a ruler connected to the end of the spring.
The ruler is marked off in a way that we can, to some accuracy, assign a number to where the red arrow points. But how closely can we read where the pointer is pointing?
Here is the experiment figure again.
Look at the ruler and notice that the divisions are spaced at ten units. When you run the experiment, you must estimate the length readings based on these divisions. No matter what the actual spring length is, you will not be able to estimate the ruler reading to a value closer than some fraction of the ruler marker spacing. This means that the accuracy of your measurement of spring length is limited by the fineness of the ruler's divisions.
The experiment also requires us to place lead weights on the end of the spring. These lead weights are marked by a measurement of their weight in grams. How close is this marked weight to the actual weight of the lead weight?
The whole experiment that we have shown produces a scientific law that is an approximation based on the limitations of the apparatus of the experiment. Is the approximation good enough? The answer, of course, depends upon what use we will make of the scientific law.
If we recall, earlier in the discussion, one reason for doing the experiment was to build a scale to weigh fish. If the experiment produces a scientific law that gives us usable weight readings for the fish we catch, then we can say that close to the spring length number has been satisfied.