Chapter 3, Problem 3.14P

(a)

Interpretation Introduction

Interpretation:

The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out for $\left[3.4(\pm 0.2)+2.6(\pm 0.1)\right]=?$

Concept Introduction:

Uncertainty:

Uncertainty means state of not certain in predicting a value.  In a measured value, the last digit will have associated uncertainty. Uncertainty has two values, absolute uncertainty and relative uncertainty.

Absolute uncertainty:

  Expressed the marginal value associated with a measurement

Relative uncertainty:

Compares the size of absolute uncertainty with the size of its associated measurement

  $\text{Relative uncertainty = }\frac{\text{absolute uncertainty}}{\text{magnitude of measurement}}$

For a set measurements having uncertainty values as $e_1,e_2\text{ and }{e}_3$, the uncertainty $(e_4)$ in addition and subtraction can be calculated as follows,

  $e_4=\sqrt{e_1^2+e_2^2+e_3^2}$

Percent relative uncertainty:

  $\text{Percent relative uncertainty = 100 }\times \text{ relative uncertainty}$

(b)

Interpretation Introduction

Interpretation:

The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out for $\left[3.4(\pm 0.2)\right]÷2.6\left(\pm 0.1\right)=?$

Concept Introduction:

Refer part (a).

(c)

Interpretation Introduction

Interpretation:

The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out for $\left[3.4(\pm 0.2)\times {10}^{-8}\right]÷\left[2.6(\pm 0.1)\times {10}^3\right]=?.$

Concept Introduction:

Refer part (a).

(d)

Interpretation Introduction

Interpretation:

The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out for $\left[3.4(\pm 0.2)-2.6(\pm 0.1)\right]\times 3.4(\pm 0.2)=?.$

Concept Introduction: Refer part (a).