Order each set of numbers from greatest to least: 1) 9.08, 9.8, 8.09; 2) 0.45, 1/2, 0.54; 3) 4.62, 4.26, 6.42, 6.24.

Steps to Solve

1. Compare the first set of numbers: 9.08, 9.8, and 8.09

   To determine the greatest and least, compare each number:

   • $9.8$ is greater than $9.08$ and also greater than $8.09$.
   • $9.08$ is greater than $8.09$.

   Thus, the order is: $$ 9.8 > 9.08 > 8.09 $$

2. Compare the second set of numbers: $0.45$, $\frac{1}{2}$, and $0.54$

   Convert $\frac{1}{2}$ to decimal:

   • $\frac{1}{2} = 0.5$.

   Now compare:

   • $0.54$ is greater than $0.5$.
   • $0.5$ is greater than $0.45$.

   Thus, the order is: $$ 0.54 > 0.5 > 0.45 $$

3. Compare the third set of numbers: $4.62$, $4.26$, $6.42$, and $6.24$

   Compare the first two and the last two numbers separately:

   • Between $4.62$ and $4.26$, $4.62$ is greater.
   • Between $6.42$ and $6.24$, $6.42$ is greater.

   Combine the results:

   • Therefore, the greatest number overall is $6.42$, followed by $6.24$, then $4.62$, and finally $4.26$.

   Thus, the order is: $$ 6.42 > 6.24 > 4.62 > 4.26 $$