Chapter 10, Problem 205A

(a)

Interpretation Introduction

Interpretation:

The subtraction must be expressed keeping correct number of significant figures.

Concept introduction:

For addition and subtraction, the result must be expressed keeping minimum digits after decimal as present in the given numbers.

Answer to Problem 205A

$(18.23-456.7)=-\mathrm{438.5.}$

Explanation of Solution

Out of 18.23 and 456.7 there is only one digit after decimal in 456.7. So the final result must be expressed keeping only one digit after decimal.

$(18.23-456.7)=-\mathrm{438.47.}$

To keep only one digit -438.47 can be rounded off to -438.5.

b)

Interpretation Introduction

Interpretation:

The division must be expressed keeping correct number of significant figures.

Concept introduction:

For multiplication and division the result must be expressed keeping minimum number of significant figures as present in the given numbers.

Answer to Problem 205A

$(4.233÷0.0131)=323.$

Explanation of Solution

Out of 4.233 and 0.0131 there are 3 significant figures in 0.0131. So the final result must be expressed keeping 3 significant figures.

$(4.233÷0.0131)=\mathrm{323.1.}$

To keep only one 3 significant figures 323.1 can be rounded off to 323.

c)

Interpretation Introduction

Interpretation:

The simplification must be expressed keeping correct number of significant figures.

Concept introduction:

For multiplication and division the result must be expressed keeping minimum number of significant figures as present in the given numbers.

For addition and subtraction the result must be expressed keeping minimum digits after decimal as present in the given numbers.

Answer to Problem 205A

$(82.44\times 4.92)+0.125=406.$

Explanation of Solution

$\begin{array}{l}(82.44\times 4.92)+0.125=405.6+0.125\\ =406+0.125=406.125\approx 406.\end{array}$

Out of 82.44 and 4.92 there are 3 significant figures in 4.92. So the multiplication result must be expressed keeping 3 significant figures. So after multiplication 405.6 is rounded off to 406. Now out of 406 and 0.125, there is no digit after decimal in 406. So the final result must be expressed without any digit after decimal.

So the final answer 406.125 is rounded off to 406.