Question

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.

Answer 1

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:

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