Chapter 3, Problem 14CR

Interpretation Introduction

(a)

Interpretation:

The given number should be converted to standard scientific notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$4.861903\times {10}^6$.

Explanation of Solution

First, the decimal point is moved until we have a number between $1$ and $10$. In this case, $4.861903$. Because the decimal point was moved six places to the left the power of the $10$ is $6$. Thus $4.861903\times {10}^6$.

Interpretation Introduction

(b)

Interpretation:

The given number should be converted into ordinary decimal notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$381.36$.

Explanation of Solution

$3.8136\times {10}^2=3.8136\times 100$

= $381.36$

The power of $10$ is positive $2$. That means two decimal places have been moved to the left. So in order to get the ordinary decimal number, the decimal place of the scientifically noted number should be moved by two decimal places to the right.

Interpretation Introduction

(c)

Interpretation:

The given number should be converted into ordinary decimal notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$0.0051$.

Explanation of Solution

$5.1\times {10}^{-3}=\frac{5.1}{1000}$

= $0.0051$

The power of $10$ is negative $3$. That means three decimal places have been moved to the right. So in order to get the ordinary decimal number, the decimal place of the scientifically noted number should be moved by three decimal places to the left.

Interpretation Introduction

(d)

Interpretation:

The given number should be converted to standard scientific notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$7.44\times {10}^{-4}$.

Explanation of Solution

First, the decimal point is moved until we have a number between $1$ and $10$. In this case, $7.44$. Because the decimal point was moved four places to the right, the power of the $10$ is negative $4$. Thus $7.44\times {10}^{-4}$.

Interpretation Introduction

(e)

Interpretation:

The given number should be converted to standard scientific notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$4.615\times {10}^3$.

Explanation of Solution

$8.621\times {10}^5\times 5.353\times {10}^{-3}=46.148\times {10}^2$

= $4.615\times {10}^3$

First, the decimal point is moved until we have a number between $1$ and $10$. In this case, the number we get after the first calculation is $46.148\times {10}^2$. Because the decimal point should be moved 1 places more to the right, the power of the $10$ is $3$. Thus $4.615\times {10}^3$.

Interpretation Introduction

(f)

Interpretation:

The given calculation should be done and final answer should be kept in standard scientific notation.

Concept Introduction:

Scientific notation is a method for making very large or very small numbers more compact and easier to write. Scientific notation simply expresses a number as a product of a number between $1$ and $10$ the appropriate power of $10$. The power of $10$ depends on the number of places the decimal point is moved and which direction. The number of places the decimal point is moved determines the power of $10$. The direction of the move determines whether the power of $10$ is positive or negative. If the decimal point is moved to the left, the power of $10$ is positive; if the decimal point is moved to the right, the power of $10$ is negative.

Answer to Problem 14CR

$1.527\times {10}^{-10}$.

Explanation of Solution

$\frac{6.283\times {10}^{-6} }{4.115\times {10}^4}=1.527\times {10}^{-6}\times {10}^{-4}$

= $1.527\times {10}^{-10}$.