Chapter 1, Problem 1.61AP

(a)

Interpretation Introduction

Interpretation:

The quantity $\text{1,234}\text{g}$ 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 quantity of x will be positive, if the decimal point is moved to the left.

The quantity of y will be negative, if the decimal point is moved to the right.

Answer to Problem 1.61AP

The quantity $\text{1,234}\text{g}$ in scientific notation is $\text{1}{\text{.234×10}}^{\text{3}}\text{g}\text{.}$

Explanation of Solution

The given quantity is $\text{1,234}\text{g}\text{.}$

The number of significant figures in the number $\text{1,234}\text{g}$ is four.

The coefficient is written as $\text{1}\text{.234}$ and it has four significant figures.

The decimal point is moved three places to the left to give the number $\text{1}\text{.234}\text{.}$  Since, the decimal point is moved to the left, the exponent is $\text{+3}$ and the coefficient is multiplied by ${\text{10}}^3\text{.}$

The quantity $\text{1,234}\text{g}$ in scientific notation is $\text{1}{\text{.234×10}}^{\text{3}}\text{g}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.000}\text{016}\text{2}\text{m}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.61AP

The quantity $\text{0}\text{.000}\text{016}\text{2}\text{m}$ in scientific notation is $\text{1}{\text{.62×10}}^{\text{-5}}\text{ m}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.000}\text{016}\text{2}\text{m}\text{.}$

The number of significant figures in the number $\text{0}\text{.000}\text{016}\text{2}\text{m}$ is three.

The coefficient is written as $1.62$ and it has three significant figures.

The decimal point is moved five places to the right to give the number $\mathrm{1.62.}$  Since, the decimal point is moved to the right, the exponent is $\text{-5}$ and the coefficient is multiplied by ${\text{10}}^{-5}\text{.}$

The quantity $\text{0}\text{.000}\text{016}\text{2}\text{m}$ in scientific notation is $\text{1}{\text{.62×10}}^{\text{-5}}\text{ m}\text{.}$

(c)

Interpretation Introduction

Interpretation:

The quantity $\text{5,244,000}\text{L}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.61AP

The quantity $\text{5,244,000}\text{L}$ in scientific notation is $\text{5}{\text{.244×10}}^{\text{6}}\text{L}\text{.}$

Explanation of Solution

The given quantity is $\text{5,244,000}\text{L}\text{.}$

The number of significant figures in the number $\text{5,244,000}\text{L}$ is four.

The coefficient is written as $\text{5}\text{.244}$ and it has four significant figures.

The decimal point is moved six places to the left to give the number $\text{5}\text{.244}\text{.}$  Since, the decimal point is moved to the left, the exponent is $\text{+6}$ and the coefficient is multiplied by ${\text{10}}^6\text{.}$

The quantity $\text{5,244,000}\text{L}$ in scientific notation is $\text{5}{\text{.244×10}}^{\text{6}}\text{L}\text{.}$

(d)

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.005}\text{62}\text{g}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.61AP

The quantity $\text{0}\text{.005}\text{62}\text{g}$ in scientific notation is $\text{5}{\text{.62×10}}^{\text{-3}}\text{g}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.005}\text{62}\text{g}\text{.}$

The number of significant figures in the number $\text{0}\text{.005}\text{62}\text{g}$ is three.

The coefficient is written as $\text{5}\text{.62}$ and it has three significant figures.

The decimal point is moved three places to the right to give the number $\text{5}\text{.62}\text{.}$  Since, the decimal point is moved to the right, the exponent is $-3$ and the coefficient is multiplied by ${\text{10}}^{\text{-3}}\text{.}$

The quantity $\text{0}\text{.005}\text{62}\text{g}$ in scientific notation is $\text{5}{\text{.62×10}}^{\text{-3}}\text{g}\text{.}$