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To solve the given problem, we'll calculate the total distance light travels in a year using the formula:

\[
\text{Distance} = \text{speed} \times \text{time}
\]

We are given:
- Speed of light: \( 1.9 \times 10^5 \) miles/second
- Time in a year: \( 3.2 \times 10^7 \) seconds

Let's perform the multiplication to find the distance in scientific notation.

\[
\text{Distance} = (1.9 \times 10^5) \times (3.2 \times 10^7)
\]

We can calculate the coefficient part and add the exponents for the powers of 10.

\[
1.9 \times 3.2 = 6.08
\]
\[
10^5 \times 10^7 = 10^{12}
\]

Thus, the total distance light travels in a year is:

\[
\text{Distance} = 6.08 \times 10^{12} \text{ miles}
\]

This is the answer in scientific notation.

Would you like further clarification or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the calculation change if the speed of light was measured in kilometers per second instead of miles?
2. Can you convert the total distance traveled in miles to kilometers using a conversion factor of \(1 \, \text{mile} = 1.60934 \, \text{kilometers}\)?
3. How would you calculate the time taken for light to travel from the Sun to Earth (distance: \(93 \times 10^6\) miles)?
4. What is the significance of scientific notation when dealing with large numbers like these?
5. How would the number of seconds in a year change if we used a leap year?

**Tip:** When multiplying numbers in scientific notation, always multiply the coefficients first and then add the exponents to simplify the process.

Light travels at an approximate rate of 1.9 × 10^5 mi./sec. There are about 3.2 × 10^7 seconds in a year. About how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.

Learn how to calculate the distance light travels in a year at a rate of 1.9 × 10^5 mi./sec and 3.2 × 10^7 seconds in a year. Understand the use of scientific notation to express large numbers and perform accurate calculations.

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