Describe two methods to compare \(\dfrac{13}{17}\) and \(0.82\). Which do you think is easier and why?
Convert both into (1) decimals (2) fractions.
Method 1: \(\dfrac{13}{17}\approx0.7647\lt0.82\Rightarrow 0.82\) is bigger.
Method 2: \(0.82=\dfrac{82}{100}=\dfrac{41}{50}\). Compare \(\dfrac{13}{17}\) and \(\dfrac{41}{50}\) using cross-multiplication: \(13\times50=650\), \(41\times17=697\Rightarrow \dfrac{41}{50}\gt\dfrac{13}{17}\). Many students find converting to decimals easier because it is a quick division.