The result after adding `3.8xx10^(-6)` and `4.2xx10^(-5)` with due regards to significant figures is

Options

A. `4.58xx10^(-5)`
B. `0.458xx10^(-4)`
C. `4.6xx10^(-5)`
D. `45.810^(-6)`

Answer

To solve the problem of adding \(3.8 \times 10^{-6}\) and \(4.2 \times 10^{-5}\) while considering significant figures, we can follow these steps:

### Step 1: Convert to the Same Power of Ten
First, we need to express both numbers in terms of the same power of ten. We can convert \(4.2 \times 10^{-5}\) to \(10^{-6}\):

\[ 4.2 \times 10^{-5} = 42 \times 10^{-6} \]

### Step 2: Add the Numbers
Now, we can add \(3.8 \times 10^{-6}\) and \(42 \times 10^{-6}\):

\[ 3.8 \times 10^{-6} + 42 \times 10^{-6} = (3.8 + 42) \times 10^{-6} \]

Calculating the sum:

\[ 3.8 + 42 = 45.8 \]

So, we have:

\[ 45.8 \times 10^{-6} \]

### Step 3: Determine Significant Figures
Next, we need to consider significant figures. The number \(3.8\) has 2 significant figures, and \(42\) has 2 significant figures. When adding, the result should be reported with the least number of decimal places from the numbers being added.

In this case, \(3.8\) has one decimal place, and \(42\) has no decimal places. Therefore, we round \(45.8\) to one decimal place, which gives us:

\[ 46.0 \times 10^{-6} \]

### Step 4: Final Answer
The final answer, considering significant figures, is:

\[ 4.60 \times 10^{-5} \]

### Summary
Thus, the result after adding \(3.8 \times 10^{-6}\) and \(4.2 \times 10^{-5}\) with due regard to significant figures is:

\[ \boxed{4.60 \times 10^{-5}} \]

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