Question

Evaluate (8.7x10 power of 13)+(1.2x10 power of 15)-(2x10 power of 11) Write your answer in scientific notation. show your work.

Answer 1

To evaluate the expression \( (8.7 \times 10^{13}) + (1.2 \times 10^{15}) - (2 \times 10^{11}) \), we first want to express all the terms with the same power of 10 for easier addition and subtraction. The largest power of 10 in our expression is \( 10^{15} \).

1. **Convert all terms to \( 10^{15} \)**:

- The first term, \( 8.7 \times 10^{13} \):
\[
8.7 \times 10^{13} = 8.7 \times 10^{13} \times \frac{10^2}{10^2} = 8.7 \times 10^{15} \times 10^{-2} = 0.087 \times 10^{15}
\]

- The second term, \( 1.2 \times 10^{15} \), stays the same:
\[
1.2 \times 10^{15}
\]

- The third term, \( 2 \times 10^{11} \):
\[
2 \times 10^{11} = 2 \times 10^{11} \times \frac{10^4}{10^4} = 2 \times 10^{15} \times 10^{-4} = 0.0002 \times 10^{15}
\]

Now, we can rewrite the expression:
\[
(0.087 \times 10^{15}) + (1.2 \times 10^{15}) - (0.0002 \times 10^{15})
\]

2. **Combine the terms**:
\[
(0.087 + 1.2 - 0.0002) \times 10^{15}
\]

Now, let's compute \( 0.087 + 1.2 - 0.0002 \):
- First, add \( 0.087 + 1.2 = 1.287 \)
- Then subtract \( 0.0002 \):
\[
1.287 - 0.0002 = 1.2868
\]

So, the combined value is:
\[
1.2868 \times 10^{15}
\]

3. **Express in scientific notation**:
The number \( 1.2868 \) is already in the range of \( 1 \) to \( 10 \), so the final result in scientific notation is:
\[
\boxed{1.2868 \times 10^{15}}
\]