Chapter 5, Problem 34A

(a)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 34A

The answer will be 2.04

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $\left(2.0944+0.0003233+12.22\right)/\left(7.001\right)$

Calculations of these digits are as follows:

  $\begin{array}{c}\frac{2.0944+0.0003233+12.22}{7.001}\text{=}\frac{14.3147233}{7.001}\\ =2.04466838\end{array}$

12.22 has limited to two decimal places. Thus after rounding off the answer will be 2.04

(b)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 34A

The answer will be $0.7\times {10}^3$

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $\left[\left(1.42\times {10}^2\right)+\left(1.021\times {10}^3\right)\right]/3.1\times {10}^{-1}$

Calculations of these digits are as follows:

  $\begin{array}{c}\frac{\left[\left(1.42\times {10}^2\right)+\left(1.021\times {10}^3\right)\right]}{3.1\times {10}^{-1}}=\frac{2.441\times {10}^3}{3.1}\\ =0.787419355\times {10}^3\end{array}$

3.1 is limited to one decimal place. Thus after rounding off the answer will be $0.7\times {10}^3$ .

(c)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 34A

The answer will be $5.19\times {10}^{-6}$

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $\left(9.762\times {10}^{-3}\right)/\left[\left(1.43\times {10}^2\right)+\left(4.51\times {10}^1\right)\right]$

Calculations of these digits are as follows:

  $\begin{array}{c}\frac{\left(9.762\times {10}^{-3}\right)}{\left[\left(1.43\times {10}^2\right)+\left(4.51\times {10}^1\right)\right]}\text{=}\frac{\left(9.762\times {10}^{-3}\right)}{1.881\times {10}^2}\\ =5.18979266\times {10}^{-6}\end{array}$

1.43 and 4.51 are limited to two decimal place. Thus after rounding off the answer will be $5.19\times {10}^{-6}$ .

(d)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 34A

The answer will be $\text{38}\text{.41}\times {10}^{-8}$

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are ${\left(6.1982\times {10}^{-4}\right)}^2$

Calculations of these digits are as follows:

  ${\left(6.1982\times {10}^{-4}\right)}^2\text{=38}\text{.4176832}\times {10}^{-8}$

6.1982has limited to four decimal places. Thus after rounding off the answer will be $\text{38}\text{.41}\times {10}^{-8}$