Let's solve the problem step-by-step.

Problem Setup:

• The star is $2.9 \times 10^2$ light years from Earth.
• One light year is approximately $5.9 \times 10^{12}$ miles.
• We need to determine how far the star is from Earth in miles, using scientific notation.

Step 1: Set up the calculation

Since 1 light year = $5.9 \times 10^{12}$ miles, the total distance to the star will be:
$(2.9 \times 10^2) \times (5.9 \times 10^{12})$

Step 2: Multiply the numbers

First, multiply the coefficients (the numbers in front):
$2.9 \times 5.9 = 17.11$

Now, multiply the powers of 10:
$10^2 \times 10^{12} = 10^{14}$

Thus, the product is:
$17.11 \times 10^{14}$

Step 3: Adjust the scientific notation

We need to express $17.11 \times 10^{14}$ in proper scientific notation (with one digit before the decimal point).
$17.11 \times 10^{14} = 1.711 \times 10^{15}$

Final Answer

The star is approximately:
$1.711 \times 10^{15} \, \text{miles}$
from Earth.

Would you like further details or clarification on any step?

Related Questions

1. How do you multiply two numbers in scientific notation more quickly?
2. What is the meaning of scientific notation, and when is it used?
3. How would the answer change if the star was $3.5 \times 10^3$ light years away?
4. What are the advantages of using scientific notation for astronomical distances?
5. How does the speed of light relate to the concept of a light year?

Tip:
When multiplying numbers in scientific notation, handle the coefficients and powers of 10 separately, then adjust to ensure one non-zero digit is to the left of the decimal.