Chapter 5, Problem 22A

Interpretation Introduction

Interpretation: The reason for the third digit of the pin length to be uncertain needs to be explained.

Concept Introduction: Each time a measurement is performed with a tool like a ruler or a graduated cylinder, an estimate is needed. In measuring devices, measurement uncertainty is the result of imprecision and uncertainty.

Answer to Problem 22A

The third digit is uncertain because in the measuring scale the smallest marked scale division is $\frac{1}{10}$ . The length of the pin is 2.85 as it is halfway or in between the smallest labeled scale range.

Explanation of Solution

From the diagram, the pin is a little longer than 2.8 cm and shorter than 2.9 cm. On the ruler between 2.8 and 2.9, there are almost no commencements so; the pin’s length between 2.8 and 2.9 cm is estimated.

  

Between 2.8 and 2.9, which correspond to 5 from 10 imaginary divisions, the end of the pin seems to come about halfway. So, the pin’s length is estimated at 2.85 cm. The last digit in this estimation is based on visual estimation. In this measurement, the first two numbers are certain numbers because both numbers are the same. The third digit is an uncertain number so; it is estimated and changes over time.

Conclusion

The uncertainty of a measurement is based on the measuring instrument.