Chapter 2, Problem 1SC

The volume of a liquid can be measured with a piece of laboratory glass ware called a graduated cylinder. If a particular volume measurement using a graduated cylinder is reported as $\text{23}\text{.4 mL,}$ what is the degree of uncertainty associated with the measurement?

$\begin{array}{l}\begin{array}{l}\text{a}\text{. ± 1 mL}\hfill \\ \text{b}\text{. ± 0}\text{.1 mL}\hfill \\ \text{c}\text{. ± 0}\text{.01 mL}\hfill \end{array}\\ \text{d}\text{. ± 0}\text{.001 mL}\end{array}$

Interpretation Introduction

Interpretation:

The degree of uncertainty in measuring the volume of a graduated cylinder is to be predicted.

Concept introduction:

In a reported quantity, all the digits are taken to be certain, except the last digit of the quantity.

The last digit is estimated and thus, it tells about the uncertainty in the measurement.

Answer to Problem 1SC

Solution: Option (b).

Explanation of Solution

Given information: The reported volume measured is $23.4\text{ mL}$

Reason for correct option:

In the given quantity, 23.4 mL, the digit 2 is at the ten’s place, the digit 3 is at the unit’s place and the digit 4 is at the tenth’s place.

The last digit in the given quantity is reported as 4, which is at the tenth’s place. So, the degree of uncertainty should be $\pm \frac{1}{10}\text{th}$ or $\pm 0.1$.

The $\pm$ sign in front of uncertainty shows that the estimated value could either be higher or lower, depending upon the measurement errors.

Hence, option (b) is correct.

Reason for incorrect options:

Option (a) is incorrect because the last digit of the quantity is at the tenth’s place and not at the unit’s place.

Option (c) is incorrect because the uncertainty has been shown at the hundredth’s place. There is no digit at the hundredth’s place in the given quantity.

Option (d) is incorrect because the uncertainty has been shown at the thousandth’s place. There is no digit at the thousandth’s place in the given quantity.

Hence, options (a), (c), and (d) are incorrect.