Chapter 5, Problem 8A

(a)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{1}{0.00032}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $\text{3}\text{.125}\times {10}^3$ .

Explanation of Solution

The given number is $\frac{1}{0.00032}$ . Calculated value this number is as follows:

  $\frac{1}{0.00032}=3125$

The exponent is +3 because decimal point must be moved three places to the left. Scientific notation of number is as follows:

  $\text{3125}=\text{3}\text{.125}\times {10}^3$

For the number 3125 scientific numbers is $\text{3}\text{.125}\times {10}^3$ .

(b)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{{10}^3}{{10}^{-3}}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $1\times {10}^6$ .

Explanation of Solution

The given number is $\frac{{10}^3}{{10}^{-3}}$ . Calculated value this number is as follows:

  $\begin{array}{c}\frac{{10}^3}{{10}^{-3}}=1\times {10}^{\left(3-\left(-3\right)\right)}\\ =1\times {10}^6\end{array}$

Thus for $\frac{{10}^3}{{10}^{-3}}$ Scientific notation is $1\times {10}^6$ .

(c)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{{10}^3}{{10}^3}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $1\times {10}^0$ .

Explanation of Solution

The given number is $\frac{{10}^3}{{10}^3}$ . Calculated value this number is as follows:

  $\begin{array}{c}\frac{{10}^3}{{10}^3}=1\times {10}^{\left(3-3\right)}\\ =1\times {10}^0\end{array}$

Thus for $\frac{{10}^3}{{10}^3}$ Scientific notation is $1\times {10}^0$ .

(d)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{1}{55000}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $\text{1}\text{.818}\times {10}^5$ .

Explanation of Solution

The given number is $\frac{1}{55000}$ . Calculated value this number is as follows:

  $\frac{1}{55000}=0.000001818181$

The exponent is -5 because decimal point must be moved five places to the right. Scientific notation of number is as follows:

  $0.000001818181=\text{1}\text{.818}\times {10}^5$

For the number $\frac{1}{55000}$ scientific numbers is $\text{1}\text{.818}\times {10}^5$ .

(e)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{\left({10}^5\right)\left({10}^4\right)\left({10}^{-4}\right)}{\left({10}^{-2}\right)}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $1\times {10}^7$ .

Explanation of Solution

The given number is $\frac{\left({10}^5\right)\left({10}^4\right)\left({10}^{-4}\right)}{\left({10}^{-2}\right)}$ . Calculated value this number is as follows:

  $\frac{\left({10}^5\right)\left({10}^4\right)\left({10}^{-4}\right)}{\left({10}^{-2}\right)}=1\times {10}^7$

For the number $\frac{\left({10}^5\right)\left({10}^4\right)\left({10}^{-4}\right)}{\left({10}^{-2}\right)}$ scientific numbers is $1\times {10}^7$ .

(f)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{43.2}{\left(4.32\times {10}^{-5}\right)}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $\text{3}\text{.125}\times {10}^3$ .

Explanation of Solution

The given number is $\frac{43.2}{\left(4.32\times {10}^{-5}\right)}$ . Calculated value this number is as follows:

  $\begin{array}{c}\frac{43.2}{\left(4.32\times {10}^{-5}\right)}=\frac{4.32\times {10}^1}{\left(4.32\times {10}^{-5}\right)}\end{array}$

        $\begin{array}{c}={10}^1\times {10}^5\end{array}$

        $\begin{array}{c}=1\times {10}^6\end{array}$

For the number $\frac{43.2}{\left(4.32\times {10}^{-5}\right)}$ scientific numbers is $1\times {10}^6$ .

(g)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{\left(4.32\times {10}^{-5}\right)}{432}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $1\times {10}^{-7}$ .

Explanation of Solution

The given number is $\frac{\left(4.32\times {10}^{-5}\right)}{432}$ . Calculated value this number is as follows:

  $\begin{array}{c}\frac{\left(4.32\times {10}^{-5}\right)}{432}=\frac{\left(432\times {10}^{-2}\times {10}^{-5}\right)}{432}\end{array}$

        $\begin{array}{c}={10}^{-2}\times {10}^{-5}\end{array}$

        $\begin{array}{c}=1\times {10}^{-7}\end{array}$

For the number $\frac{\left(4.32\times {10}^{-5}\right)}{432}$ scientific numbers is $1\times {10}^{-7}$ .

(h)

Interpretation Introduction

Interpretation: The standard scientific notation of $\frac{1}{\left({10}^5\right)\left({10}^{-6}\right)}$ to be written.

Concept introduction:

The expression of a number as a product of a number between 1 and 10 and appropriate

Conversion from scientific notation to real number is as follows:

If n>0 then, ${\text{N×10}}^{\text{n}}\text{=N×10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}$

If n<0 then, ${\text{N×10}}^{-\text{n}}\text{=}\frac{\text{N}}{\text{10×10×}\mathrm{.......}\text{n}\left(\text{Exponent}\right)\text{times}}$

Answer to Problem 8A

Scientific notation of the numbers is $1\times {10}^1$ .

Explanation of Solution

The given number is $\frac{1}{\left({10}^5\right)\left({10}^{-6}\right)}$ . Calculated value this number is as follows:

  $\begin{array}{c}\frac{1}{\left({10}^5\right)\left({10}^{-6}\right)}=\frac{1}{{10}^{5-6}}\end{array}$

        $\begin{array}{c}=\frac{1}{{10}^{-1}}\end{array}$

        $\begin{array}{c}=1\times {10}^1\end{array}$

For the number $\frac{1}{\left({10}^5\right)\left({10}^{-6}\right)}$ scientific numbers is $1\times {10}^1$ .