Question

Solve this problem, Make sure that it is in scientific notation format prior to solving.
32.8 + (8.03 × 101-8)

Answer 1

To solve the expression \( 32.8 + (8.03 \times 10^{-8}) \), we should express everything in scientific notation first.

1. Rewrite \( 32.8 \) in scientific notation:
\[
32.8 = 3.28 \times 10^1
\]

2. Now we can represent the full expression in scientific notation:
\[
3.28 \times 10^1 + 8.03 \times 10^{-8}
\]

3. Since \( 3.28 \times 10^1 \) and \( 8.03 \times 10^{-8} \) have different powers of ten, we cannot directly add them together. We need to convert them to the same power of ten. We can choose to convert \( 3.28 \times 10^1 \) to the power of \( 10^{-8} \):
\[
3.28 \times 10^1 = 3.28 \times 10^{1-8} = 3.28 \times 10^{-7}
\]

4. Now we can rewrite the expression:
\[
3.28 \times 10^{-7} + 8.03 \times 10^{-8}
\]

5. Next, we convert \( 3.28 \times 10^{-7} \) to the same power of ten as \( 8.03 \times 10^{-8} \):
\[
3.28 \times 10^{-7} = 32.8 \times 10^{-8}
\]

6. Now we can add both terms:
\[
(32.8 + 8.03) \times 10^{-8} = 40.83 \times 10^{-8}
\]

7. Finally, we convert \( 40.83 \times 10^{-8} \) to proper scientific notation:
\[
40.83 = 4.083 \times 10^1
\]
Thus,
\[
40.83 \times 10^{-8} = 4.083 \times 10^{1-8} = 4.083 \times 10^{-7}
\]

Therefore, the final answer in scientific notation is:
\[
\boxed{4.083 \times 10^{-7}}
\]