Certainly! Let's break down the values in the given table step-by-step and provide detailed explanations.
### First Row:
1. [tex]\(\frac{1}{8} = 0.125\)[/tex]
- A simple fraction conversion. Dividing 1 by 8 gives us 0.125.
2. [tex]\(-22.3\)[/tex]
- This is already in numerical form; hence, it remains [tex]\(-22.3\)[/tex].
3. [tex]\(\sqrt{144} = 12.0\)[/tex]
- The square root of 144 is 12, as multiplying 12 by itself gives 144.
4. [tex]\( 2^5 = 32\)[/tex]
- [tex]\(2\)[/tex] raised to the power of [tex]\(5\)[/tex] (i.e., [tex]\(2 \times 2 \times 2 \times 2 \times 2\)[/tex]) equals 32.
### Second Row:
5. [tex]\(4.5\)[/tex]
- This is already in numerical form; hence, it remains [tex]\(4.5\)[/tex].
6. [tex]\(1\)[/tex]
- Again, this is already in numerical form; hence, it remains [tex]\(1\)[/tex].
7. [tex]\(\sqrt{36} = 6.0\)[/tex]
- The square root of 36 is 6, as multiplying 6 by itself gives 36.
8. [tex]\(2\)[/tex]
- This is already in numerical form; hence, it remains [tex]\(2\)[/tex].
### Third Row:
- Values [tex]\(R\)[/tex] and [tex]\(F\)[/tex] are placeholders not specified in the table, so we will use the specific calculations provided here.
### Fourth Row:
9. [tex]\(\sqrt{40} \approx 6.324555320336759\)[/tex]
- The square root of 40 is an irrational number and is approximately equal to [tex]\(6.324555320336759\)[/tex].
10. [tex]\(5 \frac{2}{5} = 5.4\)[/tex]
- A mixed number, which can be converted to a decimal. [tex]\(5 \frac{2}{5}\)[/tex] translates to [tex]\(5 + \frac{2}{5}\)[/tex]. Converting [tex]\(\frac{2}{5}\)[/tex] to decimal, we get 0.4. So, [tex]\(5 + 0.4 = 5.4\)[/tex].
11. [tex]\(0.\overline{132} \approx 0.132\)[/tex]
- This represents a repeating decimal, which is approximately 0.132 when taking the first few digits.
Therefore, the full numerical breakdown of the table is:
| [tex]\(\frac{1}{8}\)[/tex] | -22.3 | [tex]\(\sqrt{144}\)[/tex] | [tex]\(2^5\)[/tex] |
|:--:|:--:|:--:|:--:|
| 0.125 | -22.3 | 12.0 | 32 |
| 4.5 | 1 | [tex]\(\sqrt{36}\)[/tex] | 2 |
|:--:|:--:|:--:|:--:|
| 4.5 | 1 | 6.0 | 2 |
| | [tex]\(R\)[/tex] | [tex]\(F\)[/tex] |
|:--:|:--:|:--:|
| | | |
| [tex]\(\sqrt{40}\)[/tex] | [tex]\(5 \frac{2}{5}\)[/tex] | [tex]\(0 . \overline{132}\)[/tex] |
|:--:|:--:|:--:|
| 6.324555320336759 | 5.4 | 0.132 |
