1. The problem is to simplify the expression: Quality \left( 1:0.1 \frac{1}{3} \right) \sqrt{gity}. 2. First, interpret the expression inside the parentheses: $1:0.1 \frac{1}{3}$. The colon ":" often denotes a ratio, so this can be read as $1 : 0.1 \times \frac{1}{3}$. 3. Calculate the product inside the ratio: $0.1 \times \frac{1}{3} = \frac{0.1}{3} = \frac{1}{10} \times \frac{1}{3} = \frac{1}{30}$. 4. So the ratio is $1 : \frac{1}{30}$. 5. A ratio $a : b$ can be expressed as the fraction $\frac{a}{b}$, so $\frac{1}{\frac{1}{30}} = 1 \times 30 = 30$. 6. Therefore, the expression inside the parentheses simplifies to 30. 7. Now the expression is $Quality \times 30 \times \sqrt{gity}$. 8. Without further context, this is the simplified form: $30 \times Quality \times \sqrt{gity}$. Final answer: $$30 \times Quality \times \sqrt{gity}$$