Chapter 1, Problem 1.58E

Interpretation Introduction

(a)

Interpretation:

The answer of the given division is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of $M\times {10}^n$. The $M$ is any number between $1$ to $10$ written with a decimal after first non-zero digit in the number and $n$ is the exponent which may be positive or negative.

Answer to Problem 1.58E

The answer of the given division expressed by using scientific notation is $2.58\times {10}^{-5}$.

Explanation of Solution

The given question is,

$\frac{3.1\times {10}^{-3}}{1.2\times {10}^2}$

The fraction can be expressed as follows:

$\frac{a\times {10}^x}{b\times {10}^y}=\left(\frac{a}{b}\right)\left({10}^{x-y}\right)$

The answer of a given fraction can be calculated as follows:

$\begin{array}{rll}\frac{3.1\times {10}^{-3-2}}{1.2}& =& \left(\frac{3.1}{1.2}\right)\left({10}^{-5}\right)\\ & =& 2.58\times {10}^{-5}\end{array}$

Hence, the answer of the given division is $2.58\times {10}^{-5}$.

Conclusion

The answer of the given division expressed by using scientific notation is $2.58\times {10}^{-5}$.

Interpretation Introduction

(b)

Interpretation:

The answer of the given division is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of $M\times {10}^n$. The $M$ is any number between $1$ to $10$ written with a decimal after first non-zero digit in the number and $n$ is the exponent which may be positive or negative.

Answer to Problem 1.58E

The answer of the given division expressed by using scientific notation is $2.19\times {10}^2$.

Explanation of Solution

The given question is,

$\frac{7.9\times {10}^4}{3.6\times {10}^2}$

The fraction can be expressed as follows:

$\frac{a\times {10}^x}{b\times {10}^y}=\left(\frac{a}{b}\right)\left({10}^{x-y}\right)$

The answer of the given fraction can be calculated as follows:

$\begin{array}{rll}\frac{7.9\times {10}^{4-2}}{3.6}& =& \left(\frac{7.9}{3.6}\right)\left({10}^2\right)\\ & =& 2.19\times {10}^2\end{array}$

Hence, the answer of the given division is $2.19\times {10}^2$.

Conclusion

The answer of the given division expressed by using scientific notation is $2.19\times {10}^2$.

Interpretation Introduction

(c)

Interpretation:

The answer of the given division is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of $M\times {10}^n$. The $M$ is any number between $1$ to $10$ written with a decimal after first non-zero digit in the number and $n$ is the exponent which may be positive or negative.

Answer to Problem 1.58E

The answer of the given division expressed by using scientific notation is $6.35\times {10}^{-4}$.

Explanation of Solution

The given question is,

$\frac{4.7\times {10}^{-1}}{7.4\times {10}^2}$

The fraction can be expressed as follows:

$\frac{a\times {10}^x}{b\times {10}^y}=\left(\frac{a}{b}\right)\left({10}^{x-y}\right)$

The answer of the given fraction can be calculated as follows:

$\begin{array}{rll}\frac{4.7\times {10}^{-1-2}}{7.4}& =& \left(\frac{4.7}{7.4}\right)\left({10}^{-3}\right)\\ & =& 0.635\times {10}^{-3}\end{array}$

The above answer is adjusted to a standard position. The decimal is shifted one place to the right and the power of $10$ is changed from $-3$ to $-4$. Hence, the answer of the given division is $6.35\times {10}^{-4}$.

Conclusion

The answer of the given division expressed by using scientific notation is $6.35\times {10}^{-4}$.

Interpretation Introduction

(d)

Interpretation:

The answer of the given division is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of $M\times {10}^n$. The $M$ is any number between $1$ to $10$ written with a decimal after first non-zero digit in the number and $n$ is the exponent which may be positive or negative.

Answer to Problem 1.58E

The answer of the given division expressed by using scientific notation is $7.25\times {10}^{-4}$.

Explanation of Solution

The given question is,

$\frac{0.00229}{3.16}$

On division the answer obtained is $0.000725$. This number can also be expressed as $0.000725\times {10}^0$.

The above answer is adjusted to a standard position. The decimal is shifted four places to the right and the power of $10$ is changed from $0$ to $-4$. Hence, the answer of a given division expressed using scientific notation is $7.25\times {10}^{-4}$.

Conclusion

The answer of the given division expressed by using scientific notation is $7.25\times {10}^{-4}$.

Interpretation Introduction

(e)

Interpretation:

The answer of the given division is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of $M\times {10}^n$. The $M$ is any number between $1$ to $10$ written with a decimal after first non-zero digit in the number and $n$ is the exponent which may be positive or negative.

Answer to Problem 1.58E

The answer of the given division expressed by using scientific notation is $3.13\times {10}^{-2}$.

Explanation of Solution

The given question is,

$\frac{119}{3.8\times {10}^3}$

The fraction can be expressed as follows:

$\frac{a\times {10}^x}{b\times {10}^y}=\left(\frac{a}{b}\right)\left({10}^{x-y}\right)$

The answer of a given fraction can be calculated as follows:

$\begin{array}{rll}\frac{119\times {10}^{-3}}{3.8}& =& \left(\frac{119}{3.8}\right)\left({10}^{-3}\right)\\ & =& 31.3\times {10}^{-3}\end{array}$

The above answer is adjusted to a standard position. The decimal is shifted one place to the left and the power of $10$ is changed from $-3$ to $-2$. Hence, the answer of the given division is $3.13\times {10}^{-2}$.

Conclusion

The answer of the given division expressed by using scientific notation is $3.13\times {10}^{-2}$.