Question

Which of the following statements is incorrect?
A) Every measurement by measuring instrument has some error.
B) A measurement can have more accuracy & less precision and vice versa.
C) Every calculated quantity that is based on measured values has some error.
D) The magnitude of the difference between the true value of the quantity and the individual measurement value is called the relative error of the measurement.

Answer 1

To answer this query, take into consideration each option and try to verify if the written statements are true or not. We should have some basic knowledge about errors and the methods which introduce errors in the calculations. Also, we have to define the terms precision, accuracy, and relative error as mentioned in the options for better understanding.

Complete answer:
When a measuring instrument is built, its accuracy rate is high as the parts in the device are new and unused. But, as the same instruments are used over and over for a long period of time, the parts of the device wear out due to factors like friction, overloading, etc. This gives rise to the error due to the faulty construction or calibration of the measuring instrument. So the statement in option (A) is correct.

For the second option, we have to first define the terms precision and accuracy. Accuracy is the degree of closeness or the level of correctness of measurement when compared to the true value. On the other hand, precision refers to how close the set of measured values that are obtained from identical measurements of a quantity are. It is used to see how reliable and consistent the measurement of the experiment is. Therefore, a more precise measurement may not be accurate and vice versa. So, the second statement is correct.

When we put the measured quantities in the formula while experimenting, the answer most likely comes in decimal form. But, with the usage of a calculator, there is a limit up to which we can calculate the decimal places. Therefore, we have to round off our values which tends to introduce errors in the calculated value.

For the fourth option, the magnitude of the difference between the true value or actual value and the measured value in an experiment is called absolute error. The relative error is the ratio of the absolute error and the actual value of the measurement.

Therefore, the statement in option (D) is incorrect.

Note: An error is defined as the difference between the actual value of the quantity measured and the measured value by experimenting. The true value is obtained by averaging an infinite number of measured values. In real life, it is nearly impossible to get 100% actual value while experimenting as there are several other errors introduced by humans and the machines which affect the value of the measured quantity.