Light travels at an approximate rate of 1.9×105

Question

1.9
×
10
5
mi./sec. There are about 3.2×107
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 point)

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.

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

We can compute the total distance traveled by light in a year as follows:

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

Now, we multiply the coefficients and the powers of ten:

1. Multiply the coefficients: \(1.9 \times 3.2 = 6.08\)
2. Add the exponents of 10: \(10^5 \times 10^7 = 10^{5+7} = 10^{12}\)

Putting it all together, we get:

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

Thus, light travels approximately \(6.08 \times 10^{12}\) miles in a year.