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To find how far the star is from Earth in miles, we multiply the distance in light years by the number of miles in one light year.

The star's distance is given as \( 3.7 \times 10^2 \) light years, and one light year is approximately \( 5.9 \times 10^{12} \) miles.

### Calculation:
\[
\text{Distance in miles} = (3.7 \times 10^2) \times (5.9 \times 10^{12})
\]

To multiply these, we can use the properties of exponents:
\[
= 3.7 \times 5.9 \times 10^{2 + 12}
= 21.83 \times 10^{14}
\]

Now, we can rewrite \( 21.83 \times 10^{14} \) in scientific notation:
\[
= 2.183 \times 10^{15}
\]

Thus, the star is approximately \( 2.183 \times 10^{15} \) miles from Earth.

Would you like more details or have any questions? Here are some related problems to consider:

1. How many miles is 1.5 light years away from Earth?
2. What would the distance be if the star were \( 5.0 \times 10^3 \) light years away?
3. Convert \( 1.0 \times 10^4 \) light years into miles.
4. If the distance is doubled to \( 7.4 \times 10^2 \) light years, what is the new distance in miles?
5. What is the significance of the exponent in scientific notation when dealing with astronomical distances?

**Tip**: When multiplying numbers in scientific notation, always add the exponents of powers of 10!

A certain star is 3.7 × 10^2 light years from the Earth. One light year is about 5.9 × 10^12 miles. How far from the Earth (in miles) is the star?

Learn how to calculate the distance of a star that is 3.7 × 10^2 light years from Earth using scientific notation. This problem involves multiplying powers of 10 and applying properties of exponents to find the distance in miles. Suitable for Grades 9-12 students.

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