Chapter 1, Problem 45P

Interpretation Introduction

(a)

Interpretation:

The number between $4.8\times {10}^2$ and $4.44\times {10}^3$ that is larger is to be indicated.

Concept introduction:

The scientific notation is the standard method of representation of a long or tedious measurement. The number is expressed as number times ten raised to some power.

For instance, mass of a proton is conveniently expressed as $1.627\times {10}^{-27}\text{ kg}$ . The decimal is shifted to the right when the power is positive while it is negative if the decimal has been shifted to left.

While a number is written in scientific notations it is scaled down to some digit between 1 to10 ten and the places that previously contain zeroes are changed to ten raised to some power.

For example, 0.00056 is written as $5.6\times {10}^{-4}$.

Answer to Problem 45P

  $4.44\times {10}^3$ is larger than $4.8\times {10}^2$.

Explanation of Solution

To compare the numbers they must be written in standard form as follows:

  $4.44\times {10}^3=4440$

Similarly, write the other number in standard form as follows:

  $4.8\times {10}^2=480.0$

Comparison of 4440 and 480.0 indicates that 44400 is larger than 480.0hence, $4.44\times {10}^3$ is larger than $4.8\times {10}^2$.

Interpretation Introduction

(b)

Interpretation:

The number between $5.6\times {10}^{-5}$ and $5.6\times {10}^{-6}$ that is larger is to be indicated.

Concept introduction:

The scientific notation is the standard method of representation of a long or tedious measurement. The number is expressed as number times ten raised to the power, where the power is the number of places decimal has been shifted. The decimal is shifted to right when the power is positive while it is negative if the decimal has been shifted to left.

While a number is written in scientific notations it is scaled down to some digit between 1 to10 ten and the places that previously contain zeroes are changed to ten raised to some power.

For example, 0.00056 is written as $5.6\times {10}^{-4}$.

Answer to Problem 45P

  $5.6\times {10}^{-5}$ is larger than $5.6\times {10}^{-6}$.

Explanation of Solution

To explicitly compare the numbers write the number in standard form as follows:

  $5.6\times {10}^{-5}=0.000056$

Similarly, write the other number in standard form as follows:

  $5.6\times {10}^{-6}=0.0000056$

Comparison of 0.000056 and 0.0000056 indicates that the former is larger than the latter.

Interpretation Introduction

(c)

Interpretation:

The number between $1.3\times {10}^8$ and52300000.0 that is larger is to be indicated.

Concept introduction:

The scientific notation is the standard method of representation of a long or tedious measurement. The number is expressed as number times ten raised to some power.

For instance, mass of a proton is conveniently expressed as $1.627\times {10}^{-27}\text{ kg}$ . The decimal is shifted to the right when the power is positive while it is negative if the decimal has been shifted to left.

While a number is written in scientific notations it is scaled down to some digit between 1 to10 ten and the places that previously contain zeroes are changed to ten raised to some power.

Answer to Problem 45P

  $1.3\times {10}^8$ is larger than 52300000.0.

Explanation of Solution

To explicitly compare the numbers write the number in standard form as follows:

  $1.3\times {10}^8=130000000.0$

Similarly, write the other number in standard form as follows:

  $52300000.0=5.23\times {10}^7$

Comparison of 52300000.0 and 130000000.0 indicates that the former is smaller than the latter.

Interpretation Introduction

(d)

Interpretation:

The number between $9.8\times {10}^{-4}$ and0.000089that is larger is to be indicated.

Concept introduction:

The scientific notation is the standard method of representation of a long or tedious measurement. The number is expressed as number times ten raised to some power.

For instance,mass of a proton is conveniently expressed as $1.627\times {10}^{-27}\text{ kg}$ . The decimal is shifted to the right when the power is positive while it is negative if the decimal has been shifted to left.

While a number is written in scientific notations it is scaled down to some digit between 1 to10 ten and the places that previously contain zeroes are changed to ten raised to some power.

Answer to Problem 45P

  $9.8\times {10}^{-4}$ is larger than 0.000089.

Explanation of Solution

To explicitly compare the numbers write the number in standard form as follows:

  $9.8\times {10}^{-4}=0.00098$

The other number isgiven in the standard form as follows:

0.000089

Comparison of 0.00098 and 0.000089 indicates that the former is larger than the latter.