Question

8.03*10to the power of -8 and multiply it with 256.7 show your work

Answer 1

To multiply \( 8.03 \times 10^{-8} \) by \( 256.7 \), you can follow these steps:

1. **Multiply the significant figures**:
\[
8.03 \times 256.7
\]

When you perform this multiplication:
\[
8.03 \times 256.7 \approx 2057.821
\]

2. **Now account for the power of 10**:
Since we have a power of \( 10^{-8} \), we can express the result of the multiplication as:
\[
2057.821 \times 10^{-8}
\]

3. **Convert to scientific notation**:
To convert \( 2057.821 \) into scientific notation, we move the decimal place to the left, which gives:
\[
2.057821 \times 10^3
\]

Therefore:
\[
2057.821 \times 10^{-8} = 2.057821 \times 10^3 \times 10^{-8} = 2.057821 \times 10^{-5}
\]

4. **Final result**:
Rounding to three significant figures (as in the original number, 8.03), we get:
\[
\approx 2.06 \times 10^{-5}
\]

So the final answer is:
\[
2.06 \times 10^{-5}
\]