Chapter 1, Problem 1.60E

Interpretation Introduction

(a)

Interpretation:

The answer of the given calculation 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 1.60E

The answer of the given calculation expressed by using scientific notation is $1.74\times {10}^{-1}$.

Explanation of Solution

The given question is,

$\frac{\left(5.3\right)\left(0.22\right)}{\left(6.1\right)\left(1.1\right)}$

Firstly, the numerator and denominator terms are solved separately and then the division is carried out as shown below.

$\begin{array}{rll}\frac{\left(5.3\right)\left(0.22\right)}{\left(6.1\right)\left(1.1\right)}& =& \frac{1.166}{6.71}\\ & =& 0.174\end{array}$

The answer of the given fraction is $0.174$ and it can also be expressed as $0.174\times {10}^0$.

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 $0$ to $-1$. Hence, the answer of a given fraction is $1.74\times {10}^{-1}$.

Conclusion

The answer of the given calculation expressed by using scientific notation is $1.74\times {10}^{-1}$.

Interpretation Introduction

(b)

Interpretation:

The answer of the given calculation 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 1.60E

The answer of the given calculation expressed by using scientific notation is $1.02\times {10}^{-9}$.

Explanation of Solution

The given question is,

$\frac{\left(3.8\times {10}^{-4}\right)\left(1.7\times {10}^{-2}\right)}{6.3\times {10}^3}$

The fraction can be expressed as follows:

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

Firstly, the numerator term is solved separately and then the division is carried out as shown below.

$\begin{array}{rll}\frac{\left(3.8\times 1.7\right)\left({10}^{-4-2}\right)}{6.3\times {10}^3}& =& \left(\frac{6.46}{6.3}\right)\left({10}^{-6-3}\right)\\ & =& 1.02\times {10}^{-9}\end{array}$

Hence, the answer of a given fraction is $1.02\times {10}^{-9}$.

Conclusion

The answer of the given calculation expressed by using scientific notation is $1.02\times {10}^{-9}$.

Interpretation Introduction

(c)

Interpretation:

The answer of the given calculation 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 1.60E

The answer of the given calculation expressed by using scientific notation is $2.59\times {10}^6$.

Explanation of Solution

The given question is,

$\frac{\left(4.8\times {10}^6\right)}{\left(7.4\times {10}^3\right)\left(2.5\times {10}^{-4}\right)}$

The fraction can be expressed as follows:

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

Firstly, the denominator term is solved separately and then the division is carried out as shown below.

$\begin{array}{rll}\frac{\left(4.8\times {10}^6\right)}{\left(7.4\times 2.5\right)\left(\times {10}^{3-4}\right)}& =& \left(\frac{4.8}{18.5}\right)\left({10}^{6+1}\right)\\ & =& 0.259\times {10}^7\end{array}$

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 $7$ to $6$. Hence, the answer of a given fraction is $2.59\times {10}^6$.

Conclusion

The answer of the given calculation expressed by using scientific notation is $2.59\times {10}^6$.

Interpretation Introduction

(d)

Interpretation:

The answer of the given calculation 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 1.60E

The answer of the given calculation expressed by using scientific notation is $2.33\times {10}^0$.

Explanation of Solution

The given question is,

$\frac{5.6}{\left(0.022\right)\left(109\right)}$

Firstly, the denominator term is solved separately and then the division is carried out as shown below.

$\begin{array}{rll}\frac{5.6}{\left(0.022\right)\left(109\right)}& =& \left(\frac{5.6}{2.398}\right)\\ & =& 2.33\end{array}$

Thus, the answer of a given fraction is $2.33$. This number expressed by using scientific notation is $2.33\times {10}^0$.

Conclusion

The answer of the given calculation expressed by using scientific notation is $2.33\times {10}^0$.

Interpretation Introduction

(e)

Interpretation:

The answer of the given calculation 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 1.60E

The answer of the given calculation expressed by using scientific notation is $1.52\times {10}^7$.

Explanation of Solution

The given question is,

$\frac{\left(4.6\times {10}^{-3}\right)\left(2.3\times {10}^2\right)}{\left(7.4\times {10}^{-4}\right)\left(9.4\times {10}^{-5}\right)}$

The fraction can be expressed as follows:

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

Firstly, the numerator and denominator terms are solved separately and then the division is carried out as shown below.

$\begin{array}{rll}\frac{\left(4.6\times 2.3\right)\left(\times {10}^{2-3}\right)}{\left(7.4\times 9.4\right)\left(\times {10}^{-5-4}\right)}& =& \left(\frac{10.58}{69.56}\right)\left({10}^{-1+9}\right)\\ & =& 0.152\times {10}^8\end{array}$

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 $8$ to $7$. Hence, the answer of a given fraction is $1.52\times {10}^7$.

Conclusion

The answer of the given calculation expressed by using scientific notation is $1.52\times {10}^7$.