Chapter E, Problem 1E

To determine

(a)

To convert:

The quantity $12\text{feet}$ into yards using dimensional analysis.

Answer to Problem 1E

Solution:

The quantity $12\text{feet}$ into yards using dimensional analysis is $4\text{yards}$.

Explanation of Solution

Given:

The given quantity is $12\text{feet}$.

Approach:

From standard conversion $1\text{yard}$ is equal to $3\text{feet}$.

Calculation:

Convert the standard conversion into fraction.

$1\text{yard}=3\text{feet}$

Divide both side with $3\text{feet}$ in the above equation.

$\begin{array}{rll}\frac{1\text{yard}}{3\text{feet}}& =& \frac{\cancel{3}\cancel{\text{feet}}}{\cancel{3}\cancel{\text{feet}}}\\ & =& 1\end{array}$ $\mathrm{.....}\left(1\right)$

Convert the feet into yard.

$12\text{feet}=12\text{feet}\times 1$

Substitute equation $\left(1\right)$ in the above equation.

$\begin{array}{rll}12\text{feet}& =& 12\cancel{\text{feet}}\times \left(\frac{1\text{yard}}{3\cancel{\text{feet}}}\right)\\ & =& 4\text{yards}\end{array}$

Therefore, the quantity $12\text{feet}$ in yards is $4\text{yards}$.

Conclusion:

Hence, the quantity $12\text{feet}$ into yards using dimensional analysis is $4\text{yards}$.

To determine

(b)

To convert:

The quantity $12\text{yards}$ into feet using dimensional analysis.

Answer to Problem 1E

Solution:

The quantity $12\text{yards}$ into feet using dimensional analysis is $36\text{feet}$.

Explanation of Solution

Given:

The given quantity is $12\text{yards}$.

Approach:

From standard conversion $1\text{yard}$ is equal to $3\text{feet}$.

Calculation:

Convert the standard conversion into fraction.

$1\text{yard}=3\text{feet}$

Divide both side with $1\text{yard}$ in the above equation.

$\begin{array}{rll}\frac{3\text{feet}}{1\text{yard}}& =& \frac{\cancel{1}\cancel{\text{yard}}}{\cancel{1}\cancel{\text{yard}}}\\ & =& 1\end{array}$ $\mathrm{.....}\left(2\right)$

Convert the yard into feet.

$12\text{yards}=12\text{yards}\times 1$

Substitute equation $\left(2\right)$ in the above equation.

$\begin{array}{rll}12\text{yards}& =& 12\cancel{\text{yards}}\times \left(\frac{3\text{feet}}{1\cancel{\text{yard}}}\right)\\ & =& 36\text{feet}\end{array}$

Therefore, the quantity $12\text{yards}$ into feet is $36\text{feet}$.

Conclusion:

Hence, the quantity $12\text{yards}$ into feet using dimensional analysis is $36\text{feet}$.