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.

1 answer

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

The speed of light is \( 1.9 \times 10^5 \) miles per second, and there are \( 3.2 \times 10^7 \) seconds in a year.

Now, we can calculate the total distance traveled by light in a year:

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

To simplify this calculation, we can first multiply the coefficients (1.9 and 3.2) and then add the exponents (5 and 7) for the powers of 10.

Calculating the coefficients:

\[ 1.9 \times 3.2 = 6.08 \]

Adding the exponents:

\[ 10^5 \times 10^7 = 10^{5+7} = 10^{12} \]

Now combining these results:

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

So, the distance light travels in a year, expressed in scientific notation, is:

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