The sum of the given two numbers with regard to significant figures is `(5.0 xx 10^(-8)) + (4.5xx10^(-6))` =

Options

A. `4.55 x 10^(-6)`
B. `4.5 xx10^(-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 need to express them in terms of the same exponent. We can convert \( 5.0 \times 10^{-8} \) to the same power as \( 4.5 \times 10^{-6} \).

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

### Step 2: Rewrite the addition
Now we can rewrite the addition with both numbers having the same exponent:

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

### Step 3: Combine the numbers
Now, we can combine the two numbers:

\[ (0.050 + 4.5) \times 10^{-6} = 4.55 \times 10^{-6} \]

### Step 4: Round the result to the correct number of significant figures
The original numbers \( 5.0 \times 10^{-8} \) and \( 4.5 \times 10^{-6} \) both have two significant figures. Therefore, we need to round \( 4.55 \times 10^{-6} \) to two significant figures.

Since the last digit (5) is followed by another 5, we round up the preceding digit (5) by 1:

\[ 4.55 \rightarrow 4.6 \]

Thus, the final result is:

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

### Final Answer:
\[ (5.0 \times 10^{-8}) + (4.5 \times 10^{-6}) = 4.6 \times 10^{-6} \]

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