Question

To convert 42.3 dekameters to kilometers, decide if you should multiply or divide by a power of 10.

Answer 1

there are 10 meters in a decameter, DECA=10, and KILO=1000, 1000 meters to a kilimeter, thus there are 100 decameters in a kilometer



`\bf \begin{array}{ccllll} decameter&kilometer\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 100&1\\ 42.3&x \end{array}\implies \cfrac{100}{42.3}=\cfrac{1}{x}\implies x=\cfrac{42.3\cdot 1}{100}`

Answer 2

1 dekameter is larger than kilometer so divide by power of 10

42.3 decameters = 0.423 kilometers so the power of 10 is 10^2