\( \frac{3}{10}.(\frac{1}{3})^{3}+\frac{1}{3} \)

To solve the expression \( \frac{3}{10} \cdot \left( \frac{1}{3} \right)^{3} + \frac{1}{3} \), we first need to calculate \( \left( \frac{1}{3} \right)^{3} \). Calculating \( \left( \frac{1}{3} \right)^{3} \): \[ \left( \frac{1}{3} \right)^{3} = \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{27} \] Now, substitute this value back into the expression: \[ \frac{3}{10} \cdot \frac{1}{27} + \frac{1}{3} \] Calculating \( \frac{3}{10} \cdot \frac{1}{27} \): \[ \frac{3}{10} \cdot \frac{1}{27} = \frac{3 \cdot 1}{10 \cdot 27} = \frac{3}{270} = \frac{1}{90} \quad (\text{simplifying by dividing numerator and denominator by 3}) \] Now add \( \frac{1}{90} \) and \( \frac{1}{3} \): First, we need to express \( \frac{1}{3} \) with a denominator of 90: \[ \frac{1}{3} = \frac{30}{90} \] Now we can add: \[ \frac{1}{90} + \frac{30}{90} = \frac{1 + 30}{90} = \frac{31}{90} \] Thus, the final result is: \[ \frac{31}{90} \]