The sum of the given two numbers with regard to significant figures is
`(5.0xx10^(-8)) + (4.5xx10^(-6)) = `

Options

A. `4.55xx10^(-6)`
B. `4.5xx10^(-6)`
C. `4.6xx10^(-6)`
D. `4xx10^(-6)`

Answer

To solve the problem of adding the two numbers \( (5.0 \times 10^{-8}) + (4.5 \times 10^{-6}) \) while considering significant figures, we can follow these steps:

### Step 1: Convert the numbers to the same power of ten
To add the two numbers, we should express them with the same exponent. The larger exponent is \( 10^{-6} \), so we will convert \( 5.0 \times 10^{-8} \) to this exponent.

\[ 5.0 \times 10^{-8} = 0.050 \times 10^{-6} \]

### Step 2: Rewrite the numbers for addition
Now we can rewrite the addition as:

\[ (0.050 \times 10^{-6}) + (4.5 \times 10^{-6}) \]

### Step 3: Perform the addition
Now we can add the two numbers:

\[ 0.050 + 4.5 = 4.550 \]

So, we have:

\[ 4.550 \times 10^{-6} \]

### Step 4: Determine the significant figures
Next, we need to consider the significant figures. The number \( 5.0 \times 10^{-8} \) has 2 significant figures (5 and 0), and \( 4.5 \times 10^{-6} \) also has 2 significant figures (4 and 5). When adding, the result should be rounded to the least number of decimal places.

In this case, both numbers have 1 decimal place after the decimal point.

### Step 5: Round the result
The result \( 4.550 \times 10^{-6} \) has 3 decimal places. Since we need to round it to 1 decimal place, we look at the second decimal place (5). Since it is 5 and the digit before it (4) is even, we round down, resulting in:

\[ 4.6 \times 10^{-6} \]

### Final Answer
Thus, the final answer is:

\[ \boxed{4.6 \times 10^{-6}} \]

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