What is the value of `(5.0 xx 10^(-6))(5.0xx10^(-8))` with due regards to significant figures ?

Options

A. `25xx10^(-14)`
B. `25.0xx10^(-14)`
C. `2.50xx10^(-13)`
D. `250xx10^(-15)`

Explanation

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

### Step 1: Identify the significant figures
Both numbers \( 5.0 \times 10^{-6} \) and \( 5.0 \times 10^{-8} \) have two significant figures.

**Hint:** Significant figures are the digits in a number that contribute to its precision. Non-zero digits are always significant, and any zeros between them or after a decimal point are also significant.

### Step 2: Perform the multiplication
Now, we multiply the two numbers:
\[ (5.0 \times 10^{-6}) \times (5.0 \times 10^{-8}) = 5.0 \times 5.0 \times 10^{-6} \times 10^{-8} \]
Calculating the coefficients:
\[ 5.0 \times 5.0 = 25.0 \]
Calculating the powers of ten:
\[ 10^{-6} \times 10^{-8} = 10^{-14} \]
Thus, we have:
\[ 25.0 \times 10^{-14} \]

**Hint:** When multiplying powers of ten, you add the exponents.

### Step 3: Adjust for significant figures
Since both original numbers had two significant figures, our result must also be expressed with two significant figures. The number \( 25.0 \) has three significant figures, so we need to round it to two significant figures, which gives us \( 25 \).

Thus, we write:
\[ 25 \times 10^{-14} \]

**Hint:** When rounding, keep only the required number of significant figures.

### Step 4: Final answer in scientific notation
We can express \( 25 \times 10^{-14} \) in proper scientific notation:
\[ 2.5 \times 10^{-13} \]

### Final Answer
The final answer, considering significant figures, is:
\[ \boxed{2.5 \times 10^{-13}} \]