Chapter 1, Problem 1.59E

Interpretation Introduction

(a)

Interpretation:

The answers of the given divisions are 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 nonexponential 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 1.59E

The answers of the given divisions expressed by using scientific notation is $1.33\times {10}^2$.

Explanation of Solution

The given question is,

$\frac{223}{1.67}$

On division the answer obtained is $133.53$. This number can also be expressed as $133.53\times {10}^0$.

The above answer is adjusted to a standard position. The decimal is shifted two places to the left and the power of $10$ is changed from $0$ to $2$. Hence, the answer of a given division expressed using scientific notation is $1.33\times {10}^2$.

Conclusion

The answers of the given divisions expressed by using scientific notation is $1.33\times {10}^2$.

Interpretation Introduction

(b)

Interpretation:

The answers of the given divisions are 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 nonexponential 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 1.59E

The answers of the given divisions expressed by using scientific notation is $1.59\times {10}^{-1}$.

Explanation of Solution

The given question is,

$\frac{6.7\times {10}^3}{4.2\times {10}^4}$

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:

$\begin{array}{rll}\frac{6.7\times {10}^{3-4}}{4.2}& =& \left(\frac{6.7}{4.2}\right)\left({10}^{-1}\right)\\ & =& 1.59\times {10}^{-1}\end{array}$

Hence, the answer of a given division is $1.59\times {10}^{-1}$.

Conclusion

The answers of the given divisions expressed by using scientific notation is $1.59\times {10}^{-1}$.

Interpretation Introduction

(c)

Interpretation:

The answers of the given divisions are 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 nonexponential 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 1.59E

The answers of the given divisions expressed by using scientific notation is $3.78\times {10}^{-2}$.

Explanation of Solution

The given question is,

$\frac{8.7\times {10}^{-4}}{2.3\times {10}^{-2}}$

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:

$\begin{array}{rll}\frac{8.7\times {10}^{-4+2}}{2.3}& =& \left(\frac{8.7}{2.3}\right)\left({10}^{-2}\right)\\ & =& 3.78\times {10}^{-2}\end{array}$

Hence, the answer of a given division is $3.78\times {10}^{-2}$.

Conclusion

The answers of the given divisions expressed by using scientific notation is $3.78\times {10}^{-2}$.

Interpretation Introduction

(d)

Interpretation:

The answers of the given divisions are 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 nonexponential 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 1.59E

The answers of the given divisions expressed by using scientific notation is $2.52\times {10}^7$.

Explanation of Solution

The given question is,

$\frac{6.8\times {10}^3}{2.7\times {10}^{-4}}$

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:

$\begin{array}{rll}\frac{6.8\times {10}^{3+4}}{2.7}& =& \left(\frac{6.8}{2.7}\right)\left({10}^7\right)\\ & =& 2.52\times {10}^7\end{array}$

Hence, the answer of a given division is $2.52\times {10}^7$.

Conclusion

The answers of the given divisions expressed by using scientific notation is $2.52\times {10}^7$.

Interpretation Introduction

(e)

Interpretation:

The answers of the given divisions are 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 nonexponential 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 1.59E

The answers of the given divisions expressed by using scientific notation is $2.77\times {10}^{-7}$.

Explanation of Solution

The given question is,

$\frac{1.8\times {10}^{-2}}{6.5\times {10}^4}$

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:

$\begin{array}{rll}\frac{1.8\times {10}^{-2-4}}{6.5}& =& \left(\frac{1.8}{6.5}\right)\left({10}^{-6}\right)\\ & =& 0.277\times {10}^{-6}\end{array}$

The above answer is adjusted to a standard position. The decimal is shifted towards one place right and the power of $10$ is changed from $-6$ to $-7$. Hence, the answer of a given division is $2.77\times {10}^{-7}$.

Conclusion

The answers of the given divisions expressed by using scientific notation is $2.77\times {10}^{-7}$.