Convert 61½ Cubic Centimeters to Cubic Decimeters: Step-by-Step Volume Conversion

Let's solve the problem through a series of steps for ease of understanding:

• Step 1: Identify the volume in cubic centimeters.
  The given volume is $61\frac{1}{2} \, \text{cm}^3$.
• Step 2: Convert the mixed number to an improper fraction.
  The mixed number $61\frac{1}{2}$ can be rewritten as $61 + \frac{1}{2}$ which equals $\frac{122}{2} + \frac{1}{2} = \frac{123}{2}$. This is equivalent to 61.5 cubic centimeters.
• Step 3: Convert cubic centimeters to cubic decimeters.
  Using the fact that $1 \, \text{dm}^3 = 1000 \, \text{cm}^3$, we divide the given volume by 1000 to convert from cubic centimeters to cubic decimeters.
  $\frac{123}{2} \div 1000 = \frac{123}{2000} = \frac{61.5}{1000}$

Therefore, the volume in cubic decimeters is $\frac{61.5}{1000} \, \text{dm}^3$.

Upon examining the available choices, choice 1: $\frac{61.5}{1000 \, \text{dm}^3}$ is the correct answer.

The solution to the problem is $\frac{61.5}{1000 \, \text{dm}^3}$.