Chapter 1, Problem 1.67AP

Write the recommended daily intake of each nutrient in scientific notation.

1. a. 0.000 400 g of folate
2. b. 0.002 g of copper
3. c. 0.000 080 g of vitamin K
4. d. 3,400 mg of chloride

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.000}\text{400}\text{g}$ of folate has to be converted into scientific notation.

Concept Introduction:

Scientific notation:

• In scientific notation, a number is represented as ${\text{y×10}}^{\text{x}}.$
• The term $\text{y,}$ is known as the coefficient, is a number ranging between $\text{1}$ and $\text{10}\text{.}$
• The term x is called as exponent that can be any positive or negative whole number.

Conversion of a Standard number to Scientific Notation:

Step 1:  The decimal point is moved to a give a number between $\text{1}$ and $\text{10}\text{.}$

Step 2:  The result is multiplied by ${\text{10}}^{\text{x}}\text{,}$ where x is the number of places the decimal point was moved.

The value of x will be positive, if the decimal point is moved to the left.

The value of x will be negative, if the decimal point is moved to the right.

Answer to Problem 1.67AP

The quantity $\text{0}\text{.000}\text{400}\text{g}$ of folate in scientific notation is $\text{4}{\text{.00×10}}^{\text{-4}}\text{g}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.000}\text{400}\text{g}$ of folate.

The number of significant figures in the number $\text{0}\text{.000}\text{400}\text{g}$ is three.

The coefficient is written as $4.00$ and it has three significant figures.

The decimal point is moved four places to the right to give the number $4.00$  Since, the decimal point is moved to the right, the exponent is $\text{-4}$ and the coefficient is multiplied by ${\text{10}}^{-4}\text{.}$

The quantity $\text{0}\text{.000}\text{400}\text{g}$ of folate in scientific notation is $\text{4}{\text{.00×10}}^{\text{-4}}\text{g}\text{.}$

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.002}\text{g}$ of copper has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.67AP

The quantity $\text{0}\text{.002}\text{g}$ of copper in scientific notation is ${\text{2×10}}^{\text{-3}}\text{g}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.002}\text{g}$ of copper.

The number of significant figures in the number $\text{0}\text{.002}\text{g}$ is one.

The coefficient is written as $\text{2}$ and it has one significant figure.

The decimal point is moved three places to the right to give the number $\text{2}\text{.}$  Since, the decimal point is moved to the right, the exponent is $\text{-3}$ and the coefficient is multiplied by ${\text{10}}^{\text{-3}}\text{.}$

The quantity $\text{0}\text{.002}\text{g}$ of copper in scientific notation is ${\text{2×10}}^{\text{-3}}\text{g}\text{.}$

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.000}\text{080}\text{g}$ of vitamin K has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.67AP

The quantity $\text{0}\text{.000}\text{080}\text{g}$ of vitamin K in scientific notation is $\text{8}{\text{.0×10}}^{\text{-5}}\text{g}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.000}\text{080}\text{g}$ of vitamin K.

The number of significant figures in the number $\text{0}\text{.000}\text{080}\text{g}$ is two.

The coefficient is written as $\text{8}\text{.0}$ and it has two significant figures.

The decimal point is moved five places to the right to give the number $\text{8}\text{.0}$  Since, the decimal point is moved to the right, the exponent is $\text{-5}$ and the coefficient is multiplied by ${\text{10}}^{\text{-5}}\text{.}$

The quantity $\text{0}\text{.000}\text{080}\text{g}$ of vitamin K in scientific notation is $\text{8}{\text{.0×10}}^{\text{-5}}\text{g}\text{.}$

Interpretation Introduction

Interpretation:

The quantity $\text{3,400}\text{mg}$ of chloride has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.67AP

The quantity $\text{3,400}\text{mg}$ of chloride in scientific notation is $\text{3}{\text{.4×10}}^{\text{3}}\text{mg}\text{.}$

Explanation of Solution

The given quantity is $\text{3,400}\text{mg}$ of chloride.

The number of significant figures in the number $\text{3,400}\text{mg}$ is two.

The coefficient is written as $\text{3}\text{.4}$ and it has two significant figures.

The decimal point is moved three places to the left to give the number $\text{3}\text{.4}\text{.}$  Since, the decimal point is moved to the left, the exponent is $+3$ and the coefficient is multiplied by ${\text{10}}^{\text{3}}\text{.}$

The quantity $\text{3,400}\text{mg}$ of chloride in scientific notation is $\text{3}{\text{.4×10}}^{\text{3}}\text{mg}\text{.}$