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

Answer 1

To find out how many miles light travels in a year, you can multiply the speed of light by the number of seconds in a year.

1. Speed of light: \( 1.9 \times 10^5 \) miles/second
2. Seconds in a year: \( 3.2 \times 10^7 \) seconds/year

Now, multiply these two values:

\[ \text{Distance} = \text{Speed} \times \text{Time} = (1.9 \times 10^5 , \text{mi/sec}) \times (3.2 \times 10^7 , \text{sec}) \]

To perform the multiplication, we can calculate the coefficients and the powers of 10 separately:

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

Now, combine these results:

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

Thus, the answer in scientific notation is:

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