Question

the table shows some data about earth. a museum has a model of earth with radius 3 meters. about how many times greater is earths actual radius than the models radius? express your answer in scientific notation. show your work. facts about earth radius at equator 6,378.1 km mass 5.8726×10²⁴ kg volume 1,083,210,000,000 km³ since 1 km = 10^ m, earths radius is about 6×10^ m. this by 3 and writing the result in scientific notation shows that earths actual radius is about times greater than the models radius. (use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Convert Earth's radius to meters

Since \(1\ km = 10^{3}\ m\), Earth's radius at the equator is \(6378.1\ km=6378.1\times10^{3}\ m\approx6.3781\times 10^{3 + 3}=6.3781\times10^{6}\ m\approx6\times 10^{6}\ m\).

Step2: Calculate the ratio

To find out how many times greater Earth's actual radius is than the model's radius, we divide Earth's radius by the model's radius. Let \(r_{1}\) be Earth's radius and \(r_{2}\) be the model's radius. We have \(\frac{r_{1}}{r_{2}}=\frac{6\times 10^{6}}{3}\).
Using the rule of exponents \(\frac{a\times10^{n}}{b}=\frac{a}{b}\times10^{n}\), we get \(\frac{6}{3}\times10^{6}=2\times10^{6}\).

Answer:

\(2\times 10^{6}\)