Express \( 2 \cdot 07 \overline{2} \) in the form \( a / b \).

To express \( 2 \cdot 07 \overline{2} \) in the form \( a / b \), we first need to understand what \( 07 \overline{2} \) means. The notation \( 07 \overline{2} \) denotes a repeating decimal, which is equivalent to \( 7.2222...\). Let’s convert \( 07 \overline{2} \) into a fraction: 1. Let \( x = 7.\overline{2} \). 2. Multiplying both sides by 10 gives us \( 10x = 72.2222...\). 3. Subtracting the first equation from the second gives \( 10x - x = 72.2222... - 7.2222... \), leading to \( 9x = 65 \). 4. Hence, \( x = \frac{65}{9} \). Now, we calculate \( 2 \cdot 07 \overline{2} \): \[ 2 \cdot 07\overline{2} = 2 \cdot \frac{65}{9} = \frac{130}{9}. \] Thus, in the form \( a / b \): \[ \boxed{\frac{130}{9}}. \]