To find out how many miles light travels in a year, we can multiply the speed of light (in miles per second) by the number of seconds in a year.
The speed of light is given as: \[ 1.9 \times 10^5 \text{ mi/sec} \]
The number of seconds in a year is given as: \[ 3.2 \times 10^7 \text{ sec/year} \]
Now we can calculate the distance light travels in one year: \[ \text{Distance} = \text{speed} \times \text{time} \] \[ \text{Distance} = (1.9 \times 10^5 \text{ mi/sec}) \times (3.2 \times 10^7 \text{ sec/year}) \]
To multiply these two scientific notations, we can multiply their coefficients and add their exponents: \[ \text{Distance} = 1.9 \times 3.2 \times 10^{5+7} \] Calculating the coefficients: \[ 1.9 \times 3.2 = 6.08 \] And adding the exponents: \[ 5 + 7 = 12 \] Thus, we have: \[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]
The final answer, in scientific notation, is: \[ \boxed{6.08 \times 10^{12}} \]
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