A star constellation is approximately `3.1times10^(4)` light years from Earth. One light year is about `5.9times10^(12)` miles. What is the approximately distance, in miles, between Earth and the constellation.

Options

A. `1.83times10^(17)`
B. `9.0times10^(49)`
C. `1.9times10^(8)`
D. `9.0times10^(16)`

Answer

To find the approximate distance in miles between Earth and the star constellation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Distance to the star constellation: \( 3.1 \times 10^4 \) light years
- Distance of one light year in miles: \( 5.9 \times 10^{12} \) miles

2. **Set Up the Conversion:**
- To find the distance in miles, we need to multiply the distance in light years by the distance of one light year in miles:
\[ \text{Distance in miles} = \text{Distance in light years} \times \text{Distance of one light year in miles} \]
\[ \text{Distance in miles} = (3.1 \times 10^4) \times (5.9 \times 10^{12}) \]

3. **Multiply the Coefficients:**
- First, multiply the numerical coefficients:
\[ 3.1 \times 5.9 = 18.29 \]

4. **Add the Exponents:**
- Next, add the exponents of 10:
\[ 10^4 \times 10^{12} = 10^{(4 + 12)} = 10^{16} \]

5. **Combine the Results:**
- Now combine the results from steps 3 and 4:
\[ \text{Distance in miles} = 18.29 \times 10^{16} \]

6. **Convert to Standard Scientific Notation:**
- To express \( 18.29 \) in proper scientific notation, we can write it as:
\[ 1.829 \times 10^1 \]
- Therefore:
\[ 18.29 \times 10^{16} = 1.829 \times 10^1 \times 10^{16} = 1.829 \times 10^{17} \]

7. **Final Result:**
- The approximate distance in miles between Earth and the constellation is:
\[ \text{Distance} \approx 1.83 \times 10^{17} \text{ miles} \]