To find out how many miles light travels in a year, we can multiply the speed of light by the number of seconds in a year.
Given:
- Speed of light: \( 1.9 \times 10^5 \) miles/second
- Seconds in a year: \( 3.2 \times 10^7 \) seconds/year
Now, we can calculate the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values:
\[ \text{Distance} = (1.9 \times 10^5 \text{ mi/sec}) \times (3.2 \times 10^7 \text{ sec}) \]
Using properties of exponents \((a \times b) \times (c \times d) = (a \times c) \times (b \times d)\):
\[ \text{Distance} = (1.9 \times 3.2) \times (10^5 \times 10^7) \]
Calculating \(1.9 \times 3.2\):
\[ 1.9 \times 3.2 = 6.08 \]
Calculating \(10^5 \times 10^7\):
\[ 10^5 \times 10^7 = 10^{5+7} = 10^{12} \]
Now, combine both results:
\[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]
Thus, in scientific notation, the distance light travels in a year is:
\[ \boxed{6.08 \times 10^{12}} \text{ miles} \]
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