To find out how far 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 per second
- Number of seconds in a year: \( 3.2 \times 10^7 \) seconds
We can calculate the distance light travels in a year as follows:
\[ \text{Distance} = (\text{Speed}) \times (\text{Time}) \] \[ \text{Distance} = (1.9 \times 10^5 , \text{mi/sec}) \times (3.2 \times 10^7 , \text{sec}) \]
To perform the multiplication, we multiply the coefficients and add the exponents:
\[ = (1.9 \times 3.2) \times (10^5 \times 10^7) \]
Calculating the coefficients:
\[ 1.9 \times 3.2 = 6.08 \]
For the exponents:
\[ 10^5 \times 10^7 = 10^{5 + 7} = 10^{12} \]
Thus, we have:
\[ \text{Distance} = 6.08 \times 10^{12} , \text{miles} \]
The final answer, in scientific notation and expressed to the exact decimal place, is:
\[ \boxed{6.08 \times 10^{12}} , \text{miles} \]
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