Let’s look at the measurement error and how it will affect the final result. Errors are presented in two types depending on their nature. They are Systematic errors (systematic uncertainties) and Random errors (random uncertainties).
Systematic errors occur due to faulty apparatus such as an incorrect scale, an incorrect zero mark on a meter, or a stopwatch that runs slowly. Repeating the measurement many times will have no effect on this type of error and it may
not even be suspected until the final result is calculated. To eliminate this type of error, a correction can be introduced to the final reading the instrument can be recalibrated or replaced.
The size of random errors depends on how well the experimenter can use the apparatus. The better the experimenter, the smaller will be the random error that will reflect in an experiment. Making a number of readings of a given quantity and taking an average will reduce the overall error.
There is a scale in the measuring instruments. It’s the least count that can be obtained from the scale. No measurements with accuracy higher than the least count. For example, the least count of the meter ruler is 1 mm. Therefore, we can’t expect a measurement with higher accuracy than 1mm from a meter ruler. That is, though we can express readings like 18.3 cm, we can’t express a reading like 18.35 cm. using a meter ruler.
The maximum error that can occur during a measurement is the least count of the scale. The size of the error needs to be considered together with the size of the quantity being measured.
(298 ± 1) and (450± 1) mm are fairly accurate measurements. (4 ± 1) and (10 ± 1) mm is highly inaccurate measurements. In order to compare error, use is made of absolute, fractional, and percentage error. For the reading (298± 1) mm; 1 mm is the absolute error, 1/298 is the fractional error (=0.0033) and 0.33% is the percentage error
As we usually require error to only one significant figure, the value 0.0033 would be used as 0.003and the value 0.33% would be used as 0.3%, respectively. The accuracy of a measurement is considered to be sufficient if the percentage error is 1 % or less than 1%.
Hence, it is considered that the accuracy obtained from a meter ruler is not sufficient in measuring lengths shorter than 10cm. In such a situation, an instrument with a least count lower than 1 mm is used. The Vernier caliper or micrometer screw gauge can be used for this. When we calculate a final result on x=an b, the error of the quantity “a” will have a greater effect on the error in x. Hence, we have to take extra care of this case.
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