Convert the following numbers to base 10: a) 3425 b) 23204 c) 101.112 d) 13.236

Here's how to convert the numbers to base 10:

a) Convert $34_5$ to base 10.

Step 1: Identify the base and digits. The number is $34_5$, which is in base 5. The digits are 3 and 4.

Step 2: Apply the conversion formula. Multiply each digit by the base raised to the power of its position. $34_5 = 3 \times 5^1 + 4 \times 5^0$

Step 3: Calculate the value. $3 \times 5 + 4 \times 1 = 15 + 4 = 19$ The number $34_5$ in base 10 is $\boxed{\text{19}}$.

b) Convert $2320_4$ to base 10.

Step 1: Identify the base and digits. The number is $2320_4$, which is in base 4. The digits are 2, 3, 2, and 0.

Step 2: Apply the conversion formula. $2320_4 = 2 \times 4^3 + 3 \times 4^2 + 2 \times 4^1 + 0 \times 4^0$

Step 3: Calculate the value. $2 \times 64 + 3 \times 16 + 2 \times 4 + 0 \times 1$ $128 + 48 + 8 + 0 = 184$ The number $2320_4$ in base 10 is $\boxed{\text{184}}$.

c) Convert $101.1_2$ to base 10.

Step 1: Identify the base and digits. The number is $101.1_2$, which is in base 2. The digits are 1, 0, 1 for the integer part and 1 for the fractional part.

Step 2: Apply the conversion formula. For digits after the decimal point, use negative powers of the base. $101.1_2 = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 + 1 \times 2^{-1}$

Step 3: Calculate the value. $1 \times 4 + 0 \times 2 + 1 \times 1 + 1 \times \frac{1}{2}$ $4 + 0 + 1 + 0.5 = 5.5$ The number $101.1_2$ in base 10 is $\boxed{\text{5.5}}$.

d) Convert $13.2_3$ to base 10.

Step 1: Analyze the number and base. The number is $13.2_3$, which is intended to be in base 3.

Step 2: Check for valid digits. In base 3, the only allowed digits are 0, 1, and 2. The number $13.2_3$ contains the digit '3'.

Step 3: Conclude validity. Since the digit '3' is present, the number $13.2_3$ is invalid in base 3 and cannot be converted.

The number $13.2_3$ is $\boxed{\text{invalid in base 3}}$.