Chapter 1, Problem 1.35P

(a)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{21}\text{.5}\text{cm}$ to $\text{m}$.

Concept Introduction:

Conversion of one unit into another unit is done by the use of unit conversion factor.  This involves multiplying or dividing by the power of 10.  For example, if centimeter has to be converted into meter, then the given value in centimeter has to be multiplied by the conversion factor as shown below.

    $1=\frac{1\text{m}}{100\text{cm}}$

Explanation of Solution

Given value is $\text{21}\text{.5}\text{cm}$.  This has to be converted into meters using the conversion factor.  Conversion factor for centimeter and meter conversion is given below.

    $\frac{1\text{m}}{100\text{cm}}or\frac{100\text{cm}}{1\text{m}}$

As the given value is in centimeter, the first conversion factor is considered.  The SI unit conversion is performed as shown below.

    $21.5\text{cm}\times \frac{1\text{m}}{100\text{cm}}=0.215\text{m}$

Therefore, the SI unit converted value of $\text{21}\text{.5}\text{cm}$ is $\text{0}\text{.215}\text{m}$.

(b)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{7}\text{.56}\times {\text{10}}^{\text{-6}}\text{m}$ to $\mu \text{m}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{7}\text{.56}\times {\text{10}}^{\text{-6}}\text{m}$.  This has to be converted into micrometers using the conversion factor.  Conversion factor for micrometer and meter conversion is given below.

    $\frac{1\mu \text{m}}{{10}^{-6}\text{m}}or\frac{{10}^{-6}\text{m}}{1\mu \text{m}}$

As the given value is in meter, the first conversion factor is considered.  The SI unit conversion is performed as shown below.

    $7.56\times {10}^{-6}\text{m}\times \frac{1\mu \text{m}}{{10}^{-6}\text{m}}=7.56\mu \text{m}$

Therefore, the SI unit converted value of $7.56\times {10}^{-6}\text{m}$ is $7.56\mu \text{m}$.

(c)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{1}\text{.2}\times {\text{10}}^{\text{-7}}\text{mg}$ to $\text{pg}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{1}\text{.2}\times {\text{10}}^{\text{-7}}\text{mg}$.  This has to be converted into picograms using the conversion factor.  Conversion factor for milligram and picogram conversion is given below.

    $\begin{array}{c}\frac{1\text{mg}}{{10}^{-3}\text{g}}or\frac{{10}^{-3}\text{g}}{1\text{mg}}\\ \text{and}\\ \frac{1\text{pg}}{{10}^{-12}\text{g}}or\frac{{10}^{-12}\text{g}}{1\text{pg}}\end{array}$

As the given value is in microgram, the conversion is done using the conversion factors as shown below.

    $\begin{array}{c}\text{1}\text{.2}\times {\text{10}}^{\text{-7}}\text{mg}\times \frac{{10}^{-3}\text{g}}{1\text{mg}}\times \frac{1\text{pg}}{{10}^{-12}\text{g}}=\frac{1.2\times {10}^{-7}\times {10}^{-3}}{{10}^{-12}}\text{pg}\\ \text{=1}\text{.2}\times {\text{10}}^{\text{2}}\text{pg}\end{array}$

Therefore, the SI unit converted value of $\text{1}\text{.2}\times {\text{10}}^{\text{-7}}\text{mg}$ is $\text{1}\text{.2}\times {\text{10}}^{\text{2}}\text{pg}$.

(d)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{15000000}\text{KB}$ to $\text{GB}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{15000000}\text{KB}$.  This has to be converted into gigabytes using the conversion factor.  Conversion factor for kilobytes and gigabytes conversion is given below.

    $\frac{1\text{GB}}{1048576\text{KB}}or\frac{1048576\text{KB}}{1\text{GB}}$

As the given value is in kilobytes, the first conversion factor is used.  This is performed as shown below.

    $\text{15000000}\text{KB}\times \frac{1\text{GB}}{1048576\text{KB}}=\text{14}\text{.30}\text{GB}$

Therefore, the SI unit converted value of $\text{15000000}\text{KB}$ is $\text{14}\text{.30}\text{GB}$.

(e)

Interpretation Introduction

Interpretation:

SI unit conversion has to be performed for $\text{6}\text{.67}{\text{mm}}^{\text{3}}$ to ${\text{cm}}^{\text{3}}$.

Concept Introduction:

Refer part (a).

Explanation of Solution

Given value is $\text{6}\text{.67}{\text{mm}}^{\text{3}}$.  This has to be converted into cubic-centimeter using the conversion factor.  Conversion factor for cubic-millimeter and cubic-centimeter conversion is given below.

    $\frac{1{\text{mm}}^{\text{3}}}{0.001{\text{cm}}^{\text{3}}}or\frac{0.001{\text{cm}}^{\text{3}}}{1{\text{mm}}^{\text{3}}}$

As the given value is in cubic-millimeter, the second conversion factor is used.  This is performed as shown below.

    $\begin{array}{c}\text{6}\text{.67}{\text{mm}}^{\text{3}}\times \frac{0.001{\text{cm}}^{\text{3}}}{1{\text{mm}}^{\text{3}}}=\text{0}\text{.00667}{\text{cm}}^{\text{3}}\\ =6.67\times {10}^{-3}{\text{cm}}^{\text{3}}\end{array}$

Therefore, the SI unit converted value of $\text{6}\text{.67}{\text{mm}}^{\text{3}}$ is $6.67\times {10}^{-3}{\text{cm}}^{\text{3}}$.