Question

the provided table shows some data about earth. express earths radius in centimeters. write your answer in scientific notation. show how you found this measurement using the laws of exponents. (1 km = 1,000 m; 1 m = 100 cm.) click the icon to view the facts about earth. since 1 km = 10□ m and 1 m = 10□ cm, the radius of earth in centimeters is 6,378.1 km = 6,378.1×10□ cm. (type integers or decimals.) written in scientific notation, earths radius in centimeters is □ cm. (use scientific notation. use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Convert km to m

Since \(1\ km = 1000\ m=10^{3}\ m\) and \(1\ m = 100\ cm = 10^{2}\ cm\), then \(1\ km=10^{3}\times10^{2}\ cm\). By the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), \(1\ km = 10^{3 + 2}=10^{5}\ cm\).

Step2: Convert Earth's radius from km to cm

The radius of Earth is \(6378.1\ km\). To convert it to cm, we multiply by the conversion factor. So \(6378.1\ km=6378.1\times10^{5}\ cm\).

Step3: Write in scientific - notation

\(6378.1\times10^{5}=6.3781\times10^{3}\times10^{5}\). Using the rule \(a^{m}\times a^{n}=a^{m + n}\) again, we get \(6.3781\times10^{3 + 5}=6.3781\times10^{8}\ cm\).

Answer:

\(6.3781\times 10^{8}\)