To multiply numbers in scientific notation, you can follow these steps:
- Multiply the coefficients (the numbers in front).
- Add the exponents of the powers of 10.
Given: \[ (8.03 \times 10^{-8}) \times (2.56 \times 10^{-2}) \]
Step 1: Multiply the coefficients \[ 8.03 \times 2.56 = 20.5588 \]
Step 2: Add the exponents \[ -8 + (-2) = -10 \]
Combining the results: \[ 20.5588 \times 10^{-10} \]
Step 3: Convert to proper scientific notation We need to express \(20.5588\) in proper scientific notation, which involves adjusting it to be between 1 and 10. We can write \(20.5588\) as: \[ 2.05588 \times 10^{1} \] So, our expression becomes: \[ 2.05588 \times 10^{1} \times 10^{-10} \]
Step 4: Combine the powers of ten \[ 2.05588 \times 10^{1 + (-10)} = 2.05588 \times 10^{-9} \]
Thus, the result of \((8.03 \times 10^{-8}) \times (2.56 \times 10^{-2})\) in scientific notation is: \[ \boxed{2.06 \times 10^{-9}} \quad (\text{rounded to three significant figures}) \]