To determine the correct inequality that compares [tex]\( 125\% \)[/tex], [tex]\( 0.47 \)[/tex], and [tex]\( 3 \frac{2}{5} \)[/tex], we will first convert all these values to decimals for a more straightforward comparison.
1. Convert [tex]\( 125\% \)[/tex] to a decimal:
[tex]\( 125\% \)[/tex] is equivalent to [tex]\( \frac{125}{100} = 1.25 \)[/tex].
2. Given [tex]\( 0.47 \)[/tex]:
The value [tex]\( 0.47 \)[/tex] is already in decimal form.
3. Convert [tex]\( 3 \frac{2}{5} \)[/tex] to a decimal:
Start by converting the mixed number to an improper fraction:
[tex]\( 3 \frac{2}{5} = 3 + \frac{2}{5} \)[/tex].
We solve [tex]\( 3 + \frac{2}{5} \)[/tex]:
[tex]\( 3 = 3.0 \)[/tex] (in decimal form)
[tex]\(\frac{2}{5} = 0.4 \)[/tex]
Adding these together:
[tex]\( 3 + 0.4 = 3.4 \)[/tex]
So now we compare:
- [tex]\( 125\% = 1.25 \)[/tex]
- [tex]\( 0.47 \)[/tex]
- [tex]\( 3 \frac{2}{5} = 3.4 \)[/tex]
When we arrange [tex]\( 0.47 \)[/tex], [tex]\( 1.25 \)[/tex], and [tex]\( 3.4 \)[/tex] in ascending order:
[tex]\[ 0.47 < 1.25 < 3.4 \][/tex]
Therefore, the correct inequality that compares these values is:
[tex]\[ 0.47 < 125\% < 3 \frac{2}{5} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{0.47 < 125\% < 3 \frac{2}{5}} \][/tex]
