Chapter 1, Problem 1.62AP

(a)

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.001}\text{25}\text{m}$ 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 1.62AP

The quantity $\text{0}\text{.001}\text{25}\text{m}$ in scientific notation is $\text{1}{\text{.25×10}}^{\text{-3}}\text{m}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.001}\text{25}\text{m}\text{.}$

The number of significant figures in the number $\text{0}\text{.001}\text{25}\text{m}$ is three.

The coefficient is written as $1.25$ and it has three significant figures.

The decimal point is moved three places to the right to give the number $\mathrm{1.25.}$  Since, the decimal point is moved to the right, the exponent is $\text{-3}$ and the coefficient is multiplied by ${\text{10}}^{-5}\text{.}$

The quantity $\text{0}\text{.001}\text{25}\text{m}$ in scientific notation is $\text{1}{\text{.25×10}}^{\text{-3}}\text{m}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The quantity $\text{8,100,000,000}\text{lb}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.62AP

The quantity $\text{8,100,000,000}\text{lb}$ in scientific notation is $\text{8}{\text{.1×10}}^{\text{9}}\text{lb}\text{.}$

Explanation of Solution

The given quantity is $\text{8,100,000,000}\text{lb}\text{.}$

The number of significant figures in the number $\text{8,100,000,000}\text{lb}$ is two.

The coefficient is written as $\text{8}\text{.1}$ and it has two significant figures.

The decimal point is moved nine 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 $\text{+9}$ and the coefficient is multiplied by ${\text{10}}^{\text{9}}\text{.}$

The quantity $\text{8,100,000,000}\text{lb}$ in scientific notation is $\text{8}{\text{.1×10}}^{\text{9}}\text{lb}\text{.}$

(c)

Interpretation Introduction

Interpretation:

The quantity $\text{54,235}\text{.6}\text{m}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.62AP

The quantity $\text{54,235}\text{.6}\text{m}$ in scientific notation is $\text{5}{\text{.42356×10}}^{\text{4}}\text{m}\text{.}$

Explanation of Solution

The given quantity is $\text{54,235}\text{.6}\text{m}\text{.}$

The number of significant figures in the number $\text{54,235}\text{.6}\text{m}$ is six.

The coefficient is written as $\text{5}\text{.42356}$ and it has six significant figures.

The decimal point is moved four places to the left to give the number $\text{5}\text{.42356}\text{.}$  Since, the decimal point is moved to the left, the exponent is $\text{+4}$ and the coefficient is multiplied by ${\text{10}}^4\text{.}$

The quantity $\text{54,235}\text{.6}\text{m}$ in scientific notation is $\text{5}{\text{.42356×10}}^{\text{4}}\text{m}\text{.}$

(d)

Interpretation Introduction

Interpretation:

The quantity $\text{0}\text{.000}\text{001}\text{899}\text{L}$ has to be converted into scientific notation.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.62AP

The quantity $\text{0}\text{.000}\text{001}\text{899}\text{L}$ in scientific notation is $\text{1}{\text{.899×10}}^{\text{-6}}\text{L}\text{.}$

Explanation of Solution

The given quantity is $\text{0}\text{.000}\text{001}\text{899}\text{L}\text{.}$

The number of significant figures in the number $\text{0}\text{.000}\text{001}\text{899}\text{L}$ is four.

The coefficient is written as $\text{1}\text{.899}$ and it has four significant figures.

The decimal point is moved six places to the right to give the number $\text{1}\text{.899}\text{.}$  Since, the decimal point is moved to the right, the exponent is $-6$ and the coefficient is multiplied by ${\text{10}}^{\text{-6}}\text{.}$

The quantity $\text{0}\text{.000}\text{001}\text{899}\text{L}$ in scientific notation is $\text{1}{\text{.899×10}}^{\text{-6}}\text{L}\text{.}$