an astronomer estimated the distance from earth to mercury to be 5.9×10^7 miles, and the distance from earth…

an astronomer estimated the distance from earth to mercury to be 5.9×10^7 miles, and the distance from earth to neptune to be 2.7×10^9 miles. he wanted to know how many times farther it is from earth to neptune than from earth to mercury. consider his work.\n1. $\frac{(2.7\times 10^{9})}{(5.9\times 10^{7})}$\n2. $(\frac{3.0}{6.0})(\frac{10^{9}}{10^{7}})$\n3. $0.5\times 10^{2}$\nthe astronomer concluded that the distance in miles from earth to neptune is 50 times the distance from earth to mercury.\nis he correct? if not, what was his mistake?\nyes, he is correct.\nno, the numerator and denominator need to be switched in the expression.\nno, he needed to round down in his estimation of the coefficients.\nno, he needed to multiple the coefficients.

an astronomer estimated the distance from earth to mercury to be 5.9×10^7 miles, and the distance from earth to neptune to be 2.7×10^9 miles. he wanted to know how many times farther it is from earth to neptune than from earth to mercury. consider his work.\n1. $\frac{(2.7\times 10^{9})}{(5.9\times 10^{7})}$\n2. $(\frac{3.0}{6.0})(\frac{10^{9}}{10^{7}})$\n3. $0.5\times 10^{2}$\nthe astronomer concluded that the distance in miles from earth to neptune is 50 times the distance from earth to mercury.\nis he correct? if not, what was his mistake?\nyes, he is correct.\nno, the numerator and denominator need to be switched in the expression.\nno, he needed to round down in his estimation of the coefficients.\nno, he needed to multiple the coefficients.

Answer

Answer:

No, the numerator and denominator need to be switched in the expression.

Explanation:

Step1: Identify the correct ratio

To find how many times farther it is from Earth to Neptune than from Earth to Mercury, we should divide the distance from Earth to Neptune by the distance from Earth to Mercury. The correct expression should be $\frac{2.7\times 10^{9}}{5.9\times 10^{7}}$, but the astronomer set it up as $\frac{5.9\times 10^{7}}{2.7\times 10^{9}}$. So the numerator and denominator are in the wrong order.