To place the given set of numbers in order from greatest to least, let's follow these steps:
1. Convert all numbers to decimal form for easy comparison:
- [tex]\( 0.21 \)[/tex] is already in decimal form: [tex]\( 0.21 \)[/tex]
- [tex]\( 22\% \)[/tex] needs to be converted to a decimal. Since [tex]\( 1\% \)[/tex] is [tex]\( 0.01 \)[/tex], [tex]\( 22\% \)[/tex] is [tex]\( 22 \times 0.01 = 0.22 \)[/tex]
- [tex]\( \frac{1}{4} \)[/tex] is a fraction. To convert it to a decimal, you divide the numerator by the denominator: [tex]\( \frac{1}{4} = 0.25 \)[/tex]
- [tex]\( 0.35 \)[/tex] is already in decimal form: [tex]\( 0.35 \)[/tex]
- [tex]\( 38\% \)[/tex] needs to be converted to a decimal. Following the same logic as for 22%, [tex]\( 38\% = 38 \times 0.01 = 0.38 \)[/tex]
- [tex]\( \frac{3}{8} \)[/tex] is a fraction. To convert it to a decimal, you divide the numerator by the denominator: [tex]\( \frac{3}{8} = 0.375 \)[/tex]
2. List the numbers in their decimal form for comparison:
- [tex]\( 0.21 \)[/tex]
- [tex]\( 0.22 \)[/tex]
- [tex]\( 0.25 \)[/tex]
- [tex]\( 0.35 \)[/tex]
- [tex]\( 0.38 \)[/tex]
- [tex]\( 0.375 \)[/tex]
3. Arrange the numbers from greatest to least:
- The greatest decimal number is [tex]\( 0.38 \)[/tex]
- Next largest is [tex]\( 0.375 \)[/tex]
- Then [tex]\( 0.35 \)[/tex]
- Followed by [tex]\( 0.25 \)[/tex]
- Next is [tex]\( 0.22 \)[/tex]
- The smallest decimal number is [tex]\( 0.21 \)[/tex]
Thus, placing the numbers from greatest to least, we have:
[tex]\[ 0.38, 0.375, 0.35, 0.25, 0.22, 0.21 \][/tex]
So, the ordered list from greatest to least is:
[tex]\[ 0.38, 0.375, 0.35, 0.25, 0.22, 0.21 \][/tex]
