The speed of light is about 1.86×10^5 miles per second. The star Sirius is about 5.062×10^13 miles from Earth. About how many seconds does it take light to travel from Sirius to Earth? Write your answer in scientific notation, rounded to the nearest hundredth.

Answer:

2.72 × 10^8 seconds

Step-by-step explanation:

1. Organize the given information to help you create the equation:

- Light travels 1.86 × 10^5 miles per 1 second

- Light travels 5.062 × 10^13 miles per n seconds

- Need to solve for n

2. Set up the equation (Make sure that both numerators and both denominators match units, so the seconds are either both on top or both on bottom, NOT switched):

[tex]\frac{1.86 * 10^5}{1}[/tex] = [tex]\frac{5.062 * 10^1^3}{n}[/tex]

3. Cross multiply (Multiply the first fraction's numerator by the second's denominator, and vice versa. It doesn't matter what number is on which side of the = sign)

n × (1.86 × 10^5) = 5.062 × 10^13

4. Solve for n by isolating the variable and dividing.

[tex]\frac{n (1.86 * 10^5)}{1.86 * 10^5}[/tex] = [tex]\frac{5.062 * 10^1^3}{1.86 * 10^5}[/tex]

n = [tex]\frac{5.062 * 10^1^3}{1.86 * 10^5}[/tex]

n = 2.72 × 10^8 (Make sure to include the unit, seconds)

The number of seconds it takes light to travel from Sirius to Earth is [tex]2.72\times10^{8}[/tex].

Given that, the speed of light is about 1.86×10^5 miles per second. The star Sirius is about 5.062×10^13 miles from Earth.

We need to find out how many seconds it takes light to travel from Sirius to Earth.

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Let the number of seconds it takes light to travel from Sirius to Earth be n seconds

Now, the proportion=[tex]\frac{1.86\times10^{5}}{1} =\frac{5.062\times10^{13}}{n}[/tex]

⇒[tex]n=\frac{5.062\times10^{13}}{1.86\times10^{5}}[/tex]

⇒[tex]n=2.72\times10^{13-5}=2.72\times10^{8}[/tex]

Therefore, the number of seconds it takes light to travel from Sirius to Earth is [tex]2.72\times10^{8}[/tex].

To learn more about scientific notation visit:

https://brainly.com/question/18073768.

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