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 many miles 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/second
- Seconds in a year: \( 3.2 \times 10^7 \) seconds/year

Now, we can calculate the distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

Substituting the values:

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

Using properties of exponents \((a \times b) \times (c \times d) = (a \times c) \times (b \times d)\):

\[
\text{Distance} = (1.9 \times 3.2) \times (10^5 \times 10^7)
\]

Calculating \(1.9 \times 3.2\):

\[
1.9 \times 3.2 = 6.08
\]

Calculating \(10^5 \times 10^7\):

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

Now, combine both results:

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

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

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