Chapter 8, Problem 1RE

For Exercises 1–16, convert each of the following using dimensional analysis.

1. $4\frac{1}{2}$ yards to feet

To determine

To convert: The given measurement to the specified equivalent unit.

Answer to Problem 1RE

Solution:

The conversion of $4\frac{1}{2}$ yards in terms of its equivalent unit is $\underset{\_}{13.5\text{ft}}$.

Explanation of Solution

Given data:

The given measurement of $4\frac{1}{2}$ yards (yd) is required to convert in terms of feet (ft).

Explanation:

Refer to the TABLE 9-1 in the text book for Units of Lengths in the English System.

From the table, write the conversion factor between feet and yards as follows.

$1\text{yd}=3\text{ft}$

Multiply with $4\frac{1}{2}$ on both sides of the expression.

$\left(1\text{yd}\right)\left(4\frac{1}{2}\right)=\left(3\text{ft}\right)\left(4\frac{1}{2}\right)$

Simplify the expression as follows.

$\begin{array}{c}4\frac{1}{2}\text{yd}=\left(3\text{ft}\right)\left(4\frac{1}{2}\right)\\ =\left(3\text{ft}\right)\left[\frac{\left(4\right)\left(2\right)+1}{2}\right]\\ =\left(3\text{ft}\right)\left(4.5\right)\\ =13.5\text{ft}\end{array}$

Thus, the conversion of $4\frac{1}{2}$ yards in terms of its equivalent unit is $\underset{\_}{13.5\text{ft}}$.