Question

1. the diameter of earth is 1.3×10^4 km. what is the diameter expressed in decimeters?

Explanation:

Step1: Recall the conversion factor

1 km = 10000 decimeters.

Step2: Multiply the given diameter by the conversion factor

$1.3\times 10^{4}\text{ km}\times10000 = 1.3\times 10^{4}\times10^{4}\text{ dm}$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $1.3\times10^{4 + 4}\text{ dm}=1.3\times 10^{8}\text{ dm}$.

Answer:

$1.3\times 10^{8}\text{ dm}$