The speed of light is approximately \( 186,000 \mathrm{mi} / \mathrm{sec} \). It takes light from a particular star approximately 4 yrs to reach Earth. How many miles away is the star from Earth? Express the answer in scientific notation. Use 365 days in 1 year. The star is \( \square \) miles away from Earth. (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal places as needed.)

Given: - The speed of light is approximately \( 186,000 \, \text{mi} / \text{sec} \). - It takes light from a particular star approximately 4 years to reach Earth. To find the distance of the star from Earth, we can use the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] First, we need to convert the time from years to seconds. There are 365 days in a year, and each day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds. Therefore, the total number of seconds in a year is: \[ 365 \times 24 \times 60 \times 60 = 31,536,000 \, \text{seconds} \] Given that it takes light 4 years to reach Earth, the total time in seconds is: \[ 4 \times 31,536,000 = 126,144,000 \, \text{seconds} \] Now, we can calculate the distance of the star from Earth using the formula: \[ \text{Distance} = 186,000 \, \text{mi} / \text{sec} \times 126,144,000 \, \text{sec} \] Let's calculate the distance. Calculate the value by following steps: - step0: Calculate: \(186000\times 126144000\) - step1: Multiply the numbers: \(23462784000000\) The distance of the star from Earth is approximately \( 2.346278 \times 10^{13} \) miles. Therefore, the star is approximately \( 2.346278 \times 10^{13} \) miles away from Earth.