Question

Divide 8.03*10 to the power of -8 and 2.56*10 to the power of -2 write answer in scientific notation

Answer 1

To divide \(8.03 \times 10^{-8}\) by \(2.56 \times 10^{-2}\), you can divide the coefficients and subtract the exponents of the powers of 10.

1. **Divide the coefficients**:
\[
\frac{8.03}{2.56} \approx 3.1375
\]

2. **Subtract the exponents**:
\[
-8 - (-2) = -8 + 2 = -6
\]

3. **Combine the results**:
\[
3.1375 \times 10^{-6}
\]

4. **Convert to scientific notation**:
The coefficient should be between 1 and 10. So, we adjust it:
\[
3.1375 = 3.1375 \times 10^0 \quad \Rightarrow \quad 3.1375 \times 10^{-6} = 0.31375 \times 10^{-5}
\]

Thus, it becomes:
\[
3.1375 \times 10^{-6} = 0.31375 \times 10^{-5} \rightarrow 3.1375 \times 10^{-6} \text{ (as is acceptable in science)}
\]

5. **Final answer in scientific notation**:
\[
\approx 3.14 \times 10^{-6} \quad \text{(rounded to three significant figures)}
\]

So, the final result is:
\[
\mathbf{3.14 \times 10^{-6}}
\]