Chapter 1, Problem 1Q

Why is it incorrect to think that the more digits you represent in your answer, the more accurate it is?

To determine

The reason for it is incorrect to think that the more digits to represent answer, more accurate it is.

Answer to Problem 1Q

The number of digits in an answer indicates the precision of the measurement it do not give more information about accuracy. Thus, it is incorrect to think that representation of a answer in more digits increases the accuracy of answer.

Explanation of Solution

Precision of a measurement indicates the reproducibility of the measurement using a given instrument. It is the degree to which repeated values are close together with the same environmental condition. Accuracy of a measurement refers the closeness of the measurement to the actual value. In a measured value or in an answer, the number of digits give the precision with which one measures the quantity. It gives very little information about the accuracy of the measurement.

If a measurement is done by great precision using an instrument which is calibrated incorrectly, then it cannot be considered as an accurate measurement. Thus, number of digits cannot give prediction about the accuracy of a measurement.

Conclusion:

Therefore, the number of digits in an answer indicates the precision of the measurement it do not give more information about accuracy. Thus, it is incorrect to think that representation of a answer in more digits increases the accuracy of answer.