4 x 10^-2 + 1.3 x 10^-1

To add the two numbers \( 4 \times 10^{-2} \) and \( 1.3 \times 10^{-1} \), we first need to express them with the same exponent.

1. Convert \( 1.3 \times 10^{-1} \) to have the same exponent as \( 4 \times 10^{-2} \): \[ 1.3 \times 10^{-1} = 1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10}{10} = 13 \times 10^{-2} \]

2. Now we can add \( 4 \times 10^{-2} \) and \( 13 \times 10^{-2} \): \[ 4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2} \]

3. Finally, we can rewrite \( 17 \times 10^{-2} \) in standard form: \[ 17 \times 10^{-2} = 0.17 \]

So, \( 4 \times 10^{-2} + 1.3 \times 10^{-1} = 0.17 \).

The result we found was \( 0.17 \). When rounded to one decimal place, it becomes \( 0.2 \).

So, the final answer expressed to one decimal place is \( 0.2 \).

I apologize for the confusion. Let's clarify:

The original summation was:

\[ 4 \times 10^{-2} + 1.3 \times 10^{-1} \]

Calculating it step by step:

1. Convert \(1.3 \times 10^{-1}\) to the same exponent as \(4 \times 10^{-2}\): \[ 1.3 \times 10^{-1} = 13 \times 10^{-2} \]

2. Now, perform the addition: \[ 4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2} \]

3. Convert to decimal form: \[ 17 \times 10^{-2} = 0.17 \]

Now, when we round \(0.17\) to one decimal place, we look at the digit in the second decimal place (which is 7) to decide whether to round up or not. Since it is 5 or more, we round up.

Thus: \[ 0.17 \text{ rounded to one decimal place is } 0.2 \]

If I made an error in interpreting your request or if you meant something else, please let me know!