Question

select the correct answer. v391 pegasi b is a star that is 4,570 light years away from earth. what is the distance in kilometers? (one light year is about 9.46 trillion kilometers.) a. 4,323 trillion kilometers b. 4,323 billion kilometers c. 43,232 kilometers d. 43,232 trillion kilometers e. 43,232 billion kilometers

Explanation:

Step1: Identify given values

Distance in light - years, \(d_{ly}=4.570\) light - years.
Distance in 1 light - year, \(d_{1ly}=9.46\) trillion kilometers \( = 9.46\times10^{12}\) kilometers.

Step2: Calculate total distance

To find the distance in kilometers, we multiply the number of light - years by the distance in one light - year.
\(d = d_{ly}\times d_{1ly}\)
Substitute \(d_{ly} = 4.570\) and \(d_{1ly}=9.46\times 10^{12}\) into the formula:
\(d=4.570\times9.46\times 10^{12}\)
First, calculate \(4.570\times9.46\):
\(4.570\times9.46=(4 + 0.57)\times9.46=4\times9.46+0.57\times9.46=37.84+5.3922 = 43.2322\)
Then, \(d = 43.2322\times10^{12}\) kilometers \(=43.2322\) trillion kilometers (since \(10^{12}\) is 1 trillion). Rounding to a reasonable number of significant figures, we get approximately 43.232 trillion kilometers.

Answer:

E. 43,232 billion kilometers (or D. 43,232 trillion kilometers, depending on the exact rounding and the options. If we consider that 1 trillion \( = 1000\) billion, \(43.232\) trillion \(=43232\) billion. But from the calculation \(4.570\times9.46\times 10^{12}=43.2322\times 10^{12}\) kilometers \( = 43.2322\) trillion kilometers, so the correct option is D (if D is 43,232 trillion kilometers) or E (if E is 43,232 billion kilometers. Since \(1\) trillion \( = 10^{12}\) and \(1\) billion \(=10^{9}\), \(43.232\times 10^{12}\) kilometers \(=43232\times 10^{9}\) kilometers \( = 43232\) billion kilometers. So the answer is E. 43,232 billion kilometers)