Chapter 10, Problem 31A

To determine

(a)

The decimal fraction of distance F over distance E.

Answer to Problem 31A

  $0.125in.$

Explanation of Solution

Given:

  

Calculation:

Since $1ft=12in.$

The figure with all the dimensions are in inches is shown below:

  

From figure the expression is written as: $\frac{E}{F}=\frac{9}{72}$

To convert it in decimal fraction, divide the numerator by the denominator.

  $\begin{array}{l}72\begin{array}{c}\hfill 0.125\\ \hfill \overline{)\begin{array}{l}90\\ \underset{\_}{72}\end{array}}\end{array}\\ 180\\ \underset{\_}{144}\\ 360\\ \underset{\_}{360}\\ 0\\ \end{array}$

Conclusion:

The decimal value is $0.125in.$

To determine

(b)

The distance 'G'.

Answer to Problem 31A

  $24in.$

Explanation of Solution

Given:

  

Calculation:

Since $1ft=12in.$

The figure with all the dimensions are in inches is shown below:

  

From figure the equation is written as: $F=E+H+G$

The length of G is calculated as

  $\begin{array}{l}F=E+H+G\\ 72=39+9+G\\ 72=48+G\\ G=72-48\\ G=24in.\end{array}$

Conclusion:

The distance G is $24in.$

To determine

(c)

The decimal fraction of distance H over distance G.

Answer to Problem 31A

  $0.6154in.$

Explanation of Solution

Given:

  

Calculation:

Since $1ft=12in.$

The figure with all the dimensions are in inches is shown below:

  

From figure the expression is written as: $\frac{G}{H}=\frac{24}{39}$

To convert it in decimal fraction, divide the numerator by the denominator.

  $\begin{array}{l}39\begin{array}{c}\hfill 0.61538\\ \hfill \overline{)\begin{array}{l}240\\ \underset{\_}{234}\end{array}}\end{array}\\ 60\\ \underset{\_}{39}\\ 21\\ \underset{\_}{195}\\ 150\\ \underset{\_}{117}\\ 330\\ \underset{\_}{312}\\ 180\\ \end{array}$

Conclusion:

The decimal value up to four places is $0.6154in.$