Light travels at an approximate rate of 1.9×10^5

Question

1.9
×
10
5
mi./sec. There are about 3.2×10^7
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)
miles

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.

Given:

• Speed of light = \( 1.9 \times 10^5 \) miles/second
• Seconds in a year = \( 3.2 \times 10^7 \) seconds/year

The calculation is as follows:

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

When multiplying the numbers in scientific notation:

1. Multiply the coefficients: \[ 1.9 \times 3.2 = 6.08 \]

2. Add the exponents: \[ 10^5 \times 10^7 = 10^{5+7} = 10^{12} \]

Combining these results:

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

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