Chapter 5, Problem 3A

(a)

Interpretation Introduction

Interpretation: The given number $6.235\times {10}^{-2}$ needs to be written as an ordinary decimal number.

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 3A

The ordinary decimal number is 0.06235.

Explanation of Solution

The given number is $6.235\times {10}^{-2}$ . Scientific notation exists of a 6.235 coefficient that is multiplied by 10 raised to an exponent -2.

Move the decimal point in the base 2 places to left, adding extra zeros as needed.

Conversions of real numbers that starts with base and divide by 2 tens is as follows:

  $\frac{6.235}{10\times 10}=0.06235$

Thus ordinary decimal number is 0.06235.

(b)

Interpretation Introduction

Interpretation: The given number $7.229\times {10}^3$ needs to be written as an ordinary decimal number.

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 3A

The ordinary decimal number is 7229.

Explanation of Solution

The given number is $7.229\times {10}^3$ . Scientific notation exists of a 7.229 coefficient that is multiplied by 10 raised to an exponent 3.

Move the decimal point in the base 3 places to left, adding extra zeros as needed.

Conversions of real numbers that starts with base and divide by 3 tens is as follows:

  $7.229\times 10\times 10\times 10=7229$

Thus ordinary decimal number is 7229.

(c)

Interpretation Introduction

Interpretation: The given number $5.001\times {10}^{-6}$ needs to be written in ordinary decimal number.

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 3A

The ordinary decimal number is 0.000005.

Explanation of Solution

The given number is $5.001\times {10}^{-6}$ . Scientific notation exists of a 5.001 coefficient that is multiplied by 10 raised to an exponent -6.

Move the decimal point in the base 6 places to left, adding extra zeros as needed.

Conversions of real numbers that starts with base and divide by 6 tens is as follows:

  $\frac{5.001}{10\times 10\times 10\times 10\times 10\times 10}=0.000005$

Thus ordinary decimal number is 0.000005.

(d)

Interpretation Introduction

Interpretation: The given number $8.621\times {10}^4$ needs to be converted into an ordinary decimal number. 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 3A

The ordinary decimal number is 86210.

Explanation of Solution

The given number is $8.621\times {10}^4$ . Scientific notation exists of an 8.621 coefficient that is multiplied by 10 raised to an exponent 4.

Move the decimal point in the base 4 places to left, adding extra zeros as needed.

Conversions of real numbers that starts with base and divide by 4 tens is as follows:

  $8.621\times 10\times 10\times 10\times 10=86210$

Thus ordinary decimal number is 86210.