Chapter 5, Problem 4A

(a)

Interpretation Introduction

Interpretation: If the number is written in standard scientific notation, the exponential value of 0.000067 to be calculated.

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 4A

The exponent value of 10 is 5.

Explanation of Solution

The given number is 0.000067. The decimal is -5 because decimal point must be moved five places to the right. Scientific notation of the number is as follows:

  $0.000067=6.7\times {10}^{-5}$

For the number 0.000067 scientific numbers is $6.7\times {10}^{-5}$ .

Thus the exponent value of 10 is 5.

(b)

Interpretation Introduction

Interpretation: If the number is written in standard scientific notation, the exponential value of 9331442 to be calculated.

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 4A

The exponent value of 10 is 6.

Explanation of Solution

The given number is 9331442. The decimal is +6 because decimal point must be moved six places to the left. Scientific notation of the number is as follows:

  $9331442=9.331442\times {10}^6$

For the number $9331442$ scientific number is $9.331442\times {10}^6$ .

Thus the exponent value of 10 is 6.

(c)

Interpretation Introduction

Interpretation: If the number is written in standard scientific notation, the exponential value of $1/10000$ to be calculated.

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 4A

The exponent value of 10 is 4.

Explanation of Solution

The given number is $1/10000$ . The decimal is -4 because decimal point must be moved four places to the right. Scientific notation of the number is as follows:

  $\frac{1}{10000}=1\times {10}^{-4}$

For the number $1/10000$ scientific numbers is $1\times {10}^{-4}$ .

Thus the exponent value of 10 is 4.

(d)

Interpretation Introduction

Interpretation: If the number is written in standard scientific notation, the exponential value of $1.631\times {10}^4$ to be calculated.

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 4A

The exponent value of 10 is 4.

Explanation of Solution

The given number is $1.631\times {10}^4$ . The decimal is +4 because decimal point must be moved four places to the right. Scientific numbers is $1.631\times {10}^4$ . Thus the exponent value of 10 is 4.