Question
Describe two methods to compare $\frac{13}{17}$ and $0.82.$ Which do you think is easier and why$?$
✓
Answer
Method $I$ convert both into decimals
$\frac{13}{17}=0.76$
$\therefore0.76<0.82$
Hence, $\frac{13}{17}<0.82$
Method $II$ Convert both into fractions
$0.82=\frac{82}{100}=\frac{41}{50}$
Now, compare $\frac{13}{17}\ \text{and}\ \frac{41}{50}$
To compare these fractions, we have to make the denominator same,
$\therefore\frac{13}{17}=\frac{13}{17}\times\frac{50}{50}=\frac{650}{850}$
$\frac{41}{50}=\frac{41}{50}\times\frac{17}{17}=\frac{697}{850}$
$\therefore\frac{697}{850}>\frac{650}{250}$
Hence, $\frac{13}{17}<0.82$
Conclusion Method $II$ is easier.
$\frac{13}{17}=0.76$
$\therefore0.76<0.82$
Hence, $\frac{13}{17}<0.82$
Method $II$ Convert both into fractions
$0.82=\frac{82}{100}=\frac{41}{50}$
Now, compare $\frac{13}{17}\ \text{and}\ \frac{41}{50}$
To compare these fractions, we have to make the denominator same,
$\therefore\frac{13}{17}=\frac{13}{17}\times\frac{50}{50}=\frac{650}{850}$
$\frac{41}{50}=\frac{41}{50}\times\frac{17}{17}=\frac{697}{850}$
$\therefore\frac{697}{850}>\frac{650}{250}$
Hence, $\frac{13}{17}<0.82$
Conclusion Method $II$ is easier.
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