Chapter 1, Problem 1.61E

Interpretation Introduction

(a)

Interpretation:

The calculations are to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and $10$ raised to some power.

Answer to Problem 1.61E

The simplified form of the given fraction is $1.75\times {10}^3$.

Explanation of Solution

The given fraction is,

$\frac{\left(7.4\times {10}^{-3}\right)\left(1.3\times {10}^4\right)}{5.5\times {10}^{-2}}$

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:

$\begin{array}{rll}\frac{7.4\times 1.3\times {10}^{-3+4}}{5.5\times {10}^{-2}}& =& \left(\frac{7.4\times 1.3}{5.5}\right)\left({10}^{1+2}\right)\\ & =& 1.75\times {10}^3\end{array}$

Hence, the simplified form of the given fraction is $1.75\times {10}^3$.

Conclusion

The simplified form of the given fraction is $1.75\times {10}^3$.

Interpretation Introduction

(b)

Interpretation:

The calculations are to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and $10$ raised to some power.

Answer to Problem 1.61E

The simplified form of the given fraction is $3.82\times {10}^5$.

Explanation of Solution

The given fraction is,

$\frac{6.4\times {10}^5}{\left(8.8\times {10}^3\right)\left(1.9\times {10}^{-4}\right)}$

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:

$\begin{array}{rll}\frac{6.4\times {10}^5}{8.8\times 1.9\times {10}^{3-4}}& =& \left(\frac{6.4}{8.8\times 1.9}\right)\left({10}^{5+1}\right)\\ & =& 0.382\times {10}^6\\ & =& 3.82\times {10}^5\end{array}$

Hence, the simplified form of the given fraction is $3.82\times {10}^5$.

Conclusion

The simplified form of the given fraction is $3.82\times {10}^3$.

Interpretation Introduction

(c)

Interpretation:

The calculations are to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and $10$ raised to some power.

Answer to Problem 1.61E

The simplified form of the given fraction is $7.67\times {10}^{-3}$.

Explanation of Solution

The given fraction is,

$\frac{\left(6.4\times {10}^{-2}\right)\left(1.1\times {10}^{-8}\right)}{\left(2.7\times {10}^{-4}\right)\left(3.4\times {10}^{-4}\right)}$

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:

$\begin{array}{rll}\frac{6.4\times 1.1\times {10}^{-2-8}}{2.7\times 3.4\times {10}^{-4-4}}& =& \left(\frac{6.4\times 1.1}{2.7\times 3.4}\right)\left({10}^{-10+8}\right)\\ & =& 0.767\times {10}^{-2}\\ & =& 7.67\times {10}^{-3}\end{array}$

Hence, the simplified form of the given fraction is $7.67\times {10}^{-3}$.

Conclusion

The simplified form of the given fraction is $7.67\times {10}^{-3}$.

Interpretation Introduction

(d)

Interpretation:

The calculations are to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and $10$ raised to some power.

Answer to Problem 1.61E

The simplified form of the given fraction is $4.338\times {10}^0$.

Explanation of Solution

The given fraction is,

$\frac{\left(963\right)\left(1.03\right)}{\left(0.555\right)\left(412\right)}$

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

$\begin{array}{rll}\frac{\left(963\right)\left(1.03\right)}{\left(0.555\right)\left(412\right)}& =& \frac{991.89}{228.660}\\ & =& 4.338\end{array}$

Hence, the simplified form of given fraction is $4.338\times {10}^0$.

Conclusion

The simplified form of the given fraction is $4.338\times {10}^0$.

Interpretation Introduction

(e)

Interpretation:

The calculations are to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers by shifting the decimal point. It is expressed as the product of a decimal term and $10$ raised to some power.

Answer to Problem 1.61E

The simplified form of the given fraction is $1.313\times {10}^1$.

Explanation of Solution

The given fraction is,

$\frac{1.15}{\left(0.12\right)\left(0.73\right)}$

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

$\frac{1.15}{\left(0.12\right)\left(0.73\right)}=\frac{1.15}{0.0876}$

The numbers are adjusted to a standard position. The decimal is shifted towards right and the power of $10$ is expressed as follows.

$\begin{array}{rll}\frac{1.15}{0.0876}& =& \frac{11.5\times {10}^{-1}}{8.76\times {10}^{-2}}\\ & =& 1.313\times {10}^1\end{array}$

Hence, the simplified form of given fraction is $1.313\times {10}^1$.

Conclusion

The simplified form of the given fraction is $1.313\times {10}^1$.