Chapter 1.5, Problem 1.20Q

(a)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\frac{\text{27}\text{.2}\text{×}\text{15}\text{.63}}{\text{1}\text{.84}}\text{=}$

Explanation of Solution

The given operation is $\frac{\text{27}\text{.2}\text{×}\text{15}\text{.63}}{\text{1}\text{.84}}\text{=}$.

The numerator is solved and the result is reported in three significant figures.

  $\text{27}\text{.2}\text{×}\text{15}\text{.63}\text{=}\text{425}\text{=}\text{4}\text{.25}\text{×}{\text{10}}^{\text{2}}$

The operation is division.  Numerator consists of three significant figures and denominator consists of three significant figures.  The result will be reported in three significant figures.

  $\frac{\text{27}\text{.2}\text{×}\text{15}\text{.63}}{\text{1}\text{.84}}\text{=}\frac{\text{425}}{\text{1}\text{.84}}\text{=}\text{231}\text{=}\text{2}\text{.31}\text{×}{\text{10}}^{\text{2}}$

(b)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\frac{\text{13}\text{.6}}{\text{18}\text{.02}\text{×}\text{1}\text{.6}}\text{=}$

Explanation of Solution

The given operation is $\frac{\text{13}\text{.6}}{\text{18}\text{.02}\text{×}\text{1}\text{.6}}\text{=}$.

The denominator is solved and the result is reported in two significant figures.

  $\text{18}\text{.02}\text{×}\text{1}\text{.6}\text{=}\text{29}\text{=}\text{2}\text{.9}\text{×}{\text{10}}^{\text{1}}$

The operation is division.  Numerator consists of three significant figures and denominator consists of two significant figures.  The result will be reported in fewer significant figures that is in two significant figures.

  $\frac{\text{13}\text{.6}}{\text{18}\text{.02}\text{×}\text{1}\text{.6}}\text{=}\frac{\text{13}\text{.6}}{\text{29}}\text{=}\text{0}\text{.47}\text{=}\text{4}\text{.7}\text{×}{\text{10}}^{\text{-1}}$

(c)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\frac{\text{4}\text{.79}\text{×}{\text{10}}^{\text{5}}}{\text{0}\text{.7911}}\text{=}$

Explanation of Solution

The given operation is $\frac{\text{4}\text{.79}\text{×}{\text{10}}^{\text{5}}}{\text{0}\text{.7911}}\text{=}$.

The numerator is converted into standard notation.

  $\text{4}\text{.79}\text{×}{\text{10}}^{\text{5}}\text{=}\text{479000}$

The operation is division.  Numerator consists of three significant figures and denominator consists of four significant figures.  The result will be reported in three significant figures.

  $\frac{\text{4}\text{.79}\text{×}{\text{10}}^{\text{5}}}{\text{0}\text{.7911}}\text{=}\frac{\text{479000}}{\text{0}\text{.7911}}\text{=}\text{605000}\text{=}\text{6}\text{.05}\text{×}{\text{10}}^{\text{5}}$

(d)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\text{3}\text{.58}\text{×}\text{4}\text{.0}\text{=}$

Explanation of Solution

The given operation is $\text{3}\text{.58}\text{×}\text{4}\text{.0}$.

The operation is multiplication.  The first value consists of three significant figures and second value consists of two significant figures.  The result will be reported in fewer significant figures that is in two significant figures.

  $\text{3}\text{.58}\text{×}\text{4}\text{.0}\text{=}\text{14}\text{=}\text{1}\text{.4}\text{×}{\text{10}}^{\text{1}}$

(e)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\frac{\text{3}\text{.58}}{\text{4}\text{.0}}\text{=}$

Explanation of Solution

The given operation is $\frac{\text{3}\text{.58}}{\text{4}\text{.0}}\text{=}$.

The operation is division.  Numerator consists of three significant figures and denominator consists of two significant figures.  The result will be reported in fewer significant figures that is in two significant figures.

  $\frac{\text{3}\text{.58}}{\text{4}\text{.0}}\text{=}\text{0}\text{.90}\text{=}\text{9}\text{.0}\text{×}{\text{10}}^{\text{-1}}$

(f)

Interpretation Introduction

Interpretation:

The result of the given operation has to be reported to the proper number of significant figures and in scientific notation.

  $\frac{\text{11}\text{.4}\text{×}{\text{10}}^{\text{-4}}}{\text{0}\text{.45}}\text{=}$

Explanation of Solution

The given operation is $\frac{\text{11}\text{.4}\text{×}{\text{10}}^{\text{-4}}}{\text{0}\text{.45}}\text{=}$.

The numerator is converted into standard notation.

  $\text{11}\text{.4}\text{×}{\text{10}}^{\text{-4}}\text{=}\text{0}\text{.000114}$

The operation is division.  Numerator consists of three significant figures and denominator consists of two significant figures.  The result will be reported in fewer significant figures that is in two significant figures.

  $\frac{\text{11}\text{.4}\text{×}{\text{10}}^{\text{-4}}}{\text{0}\text{.45}}\text{=}\frac{\text{0}\text{.000114}}{\text{0}\text{.45}}\text{=}\text{0}\text{.00025}\text{=}\text{2}\text{.5}\text{×}{\text{10}}^{\text{-4}}$