Chapter 5, Problem 5A

(a)

Interpretation Introduction

Interpretation: The scientific number of 9367421 to be determined.

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 5A

The numbers is $\text{9}\text{.367421}\times {10}^6$ .

Explanation of Solution

The given number is 9367421. The exponent is +6 because decimal point must be moved six places to the left. Scientific notation of number is as follows:

  $\text{9367421}=\text{9}\text{.367421}\times {10}^6$

For the number 9367421 scientific numbers is $\text{9}\text{.367421}\times {10}^6$ .

(b)

Interpretation Introduction

Interpretation: The scientific number of 7241 to be determined.

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 5A

The numbers is $\text{7}\text{.241}\times {10}^3$ .

Explanation of Solution

The given number is 7241. The exponent is +3 because decimal point must be moved three places to the left. Scientific notation of number is as follows:

  $\text{7241}=\text{7}\text{.241}\times {10}^3$

For the number 7241 scientific numbers is $\text{7}\text{.241}\times {10}^3$ .

(c)

Interpretation Introduction

Interpretation: The scientific number of 0.0005519 to be determined.

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 5A

The numbers is $\text{5}\text{.519}\times {10}^{-4}$ .

Explanation of Solution

The given number is 0.0005519. The exponent is -4 because decimal point must be moved four places to the left. Scientific notation of number is as follows:

  $0.000\text{5519}=\text{5}\text{.519}\times {10}^{-4}$

For the number 0.0005519 scientific numbers is $\text{5}\text{.519}\times {10}^{-4}$ .

(d)

Interpretation Introduction

Interpretation: The scientific number 5.408 to be determined.

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 5A

The numbers is $\text{5}\text{.408}\times {10}^0$ .

Explanation of Solution

The given number is 5.408. The exponent is 0 because decimal point does not have moved. Scientific notation of number is as follows:

  $\text{5}\text{.408}=\text{5}\text{.408}\times {10}^0$

For the number 9367421 scientific numbers is $\text{5}\text{.408}\times {10}^0$ .

(e)

Interpretation Introduction

Interpretation: The scientific number of $6.24\times {10}^2$ to be determined.

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 5A

The number is $6.24\times {10}^2$ .

Explanation of Solution

The given number is $6.24\times {10}^2$ . The given number is in standard scientific notation. Thus the number is $6.24\times {10}^2$ .

(f)

Interpretation Introduction

Interpretation: The scientific number of $6319\times {10}^{-2}$ to be determined.

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 5A

The numbers is $6.319\times {10}^1$ .

Explanation of Solution

The given number is $6319\times {10}^{-2}$ . The exponent is +3 because decimal point must be moved three places to the left. Scientific notation of number is as follows:

  $6.319\times {10}^{-2}\times {10}^3=6.319\times {10}^1$

For the number $6319\times {10}^{-2}$ scientific numbers is $6.319\times {10}^1$ .

Thus the exponent value of 10 is 6.

(g)

Interpretation Introduction

Interpretation: The scientific number of 0.000000007215 to be determined.

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 5A

The numbers is $7.215\times {10}^{-9}$ .

Explanation of Solution

The given number is 0.000000007215. The exponent is -9 because decimal point must be moved nine places to the left. Scientific notation of number is as follows:

  $0.00000000\text{7215}=7.215\times {10}^{-9}$

Thus the number 0.000000007215 scientific numbers is $7.215\times {10}^{-9}$ .

(h)

Interpretation Introduction

Interpretation: The scientific number of 0.721 to be determined.

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 5A

The numbers is $\text{7}\text{.21}\times {10}^{-1}$ .

Explanation of Solution

The given number is 0.721. The exponent is -1 because decimal point must be moved one places to the right. Scientific notation of number is as follows:

  $\text{0}\text{.721}=\text{7}\text{.21}\times {10}^{-1}$

For the number 0.721 scientific numbers is $\text{7}\text{.21}\times {10}^{-1}$ .