Answer :

To put the numbers in order from greatest to least, let's evaluate each of them:

1. First number: [tex]\(-4.7\)[/tex]
2. Second number: [tex]\(4\)[/tex]
3. Third number: [tex]\(-4 \frac{18}{20}\)[/tex]

Let's convert the third number into a decimal form to make it easier to compare:

- The fraction [tex]\(\frac{18}{20}\)[/tex] simplifies to [tex]\(0.9\)[/tex], so the mixed number [tex]\(-4 \frac{18}{20}\)[/tex] can be written as [tex]\(-4 + 0.9 = -3.1\)[/tex].

Now we have three values to compare:

- [tex]\(-4.7\)[/tex]
- [tex]\(4\)[/tex]
- [tex]\(-3.1\)[/tex]

To order these from greatest to least, we consider their position on the number line:

- Greatest: [tex]\(4\)[/tex] (since it's the only positive number and larger than any negative number)
- Next greatest: [tex]\(-3.1\)[/tex] (less negative compared to [tex]\(-4.7\)[/tex])
- Least: [tex]\(-4.7\)[/tex] (more negative than [tex]\(-3.1\)[/tex])

So, in order from greatest to least, the numbers are:

[tex]\[ 4, -3.1, -4.7 \][/tex]

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