Chapter 5, Problem 10A

(a)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to $1,000,000$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds $1,000,000$ is mega.

Explanation of Solution

The given number is $1,000,000$ . In 10^th power, it is written as ${10}^6$ .

  $1,000,000={10}^6$

The power of 10, in this case, is 6. Hence, the metric prefix corresponds to $1,000,000$ mega and it is denoted by the symbol M.

(b)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to

  ${10}^{-3}$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds ${10}^{-3}$ is milli.

Explanation of Solution

The given number is ${10}^{-3}$ .

  $\begin{array}{c}{10}^{-3}=\frac{1}{{10}^{-3}}\end{array}$

      $\begin{array}{c}=\frac{1}{1000}\end{array}$

  ${10}^{-3}$ is a one-thousandth part. Milli is a factor of one-thousandth. Thus, milli is the metric prefix corresponding to ${10}^{-3}$ . It is denoted by the symbol m.

(c)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to ${10}^{-9}$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds ${10}^{-9}$ is nano.

Explanation of Solution

The given number is ${10}^{-9}$ .

  $\begin{array}{c}{10}^{-9}=\frac{1}{{10}^9}\end{array}$

      $\begin{array}{c}=\frac{1}{1000000000}\end{array}$

The power of 10, in this case, is 9 and it is one billionth. Hence, the metric prefix corresponds to ${10}^{-9}$ be nano and it is denoted by symbol n.

(d)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to ${10}^6$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds ${10}^6$ is mega.

Explanation of Solution

The given number is ${10}^6$ . The prefix in this indication is 6. Hence, the metric prefix corresponds to ${10}^6$ be mega and it is denoted by the symbol M.

(e)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to ${10}^{-2}$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds ${10}^{-2}$ is centi.

Explanation of Solution

The given number is ${10}^{-2}$ .

  $\begin{array}{c}{10}^{-2}=\frac{1}{{10}^{-2}}\end{array}$

      $\begin{array}{c}=\frac{1}{100}\end{array}$

The metric prefix that corresponds to ${10}^{-2}$ is centi and it is denoted by symbol c.

(f)

Interpretation Introduction

Interpretation: The metric prefix that corresponds to $0.000001$ needs to be explained.

Concept Introduction: A metric prefix is a suffix of a unit that introduces a simple unit of measure to denote a unit multiple or submultiple. Each prefix has a unique symbol, prepended on any symbol of the unit. Since the size of the fundamental units is not always convenient, thus, the SI system uses prefixes to change the size of the unit.

Answer to Problem 10A

The metric prefix that corresponds $0.000001$ is micro.

Explanation of Solution

The given number is $0.000001$ . In 10^th power, it is written as:

  $\begin{array}{c}0.000001=\frac{1}{1000000}\end{array}$

      $\begin{array}{c}=\frac{1}{{10}^6}\end{array}$

      $\begin{array}{c}={10}^{-6}\end{array}$

The metric prefix that corresponds to $0.000001$ is micro and it is denoted by the symbol $\text{μ}$ .