Question
Each of the lists below is in order from least to greate \( \mathrm{gr}^{\mathrm{st}} \) and has one number missing. List an example of a value that could correctly complete the blank in each list. 1. \( -\sqrt{49},-\frac{33}{5} \) \( \qquad \) ,\( -6 . \overline{4} \) 2. \( \qquad \) \( , 8.75,8 \frac{4}{5}, \sqrt{81} \) 3. \( -2 \frac{9}{10} \) \( \qquad \) \( ,-2 \frac{3}{5},-2.45 \)
Ask by Guzman Byrd. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Here are the example values to complete the lists:
1. **-6.5**
2. **8.5**
3. **-2.7**
Solution
Let's analyze each list to determine a suitable value that correctly completes the blank.
### 1. \( -\sqrt{49}, -\frac{33}{5} \), **,** \(-6.\overline{4}\)
**Step-by-Step:**
- \( -\sqrt{49} = -7 \)
- \( -\frac{33}{5} = -6.6 \)
- \( -6.\overline{4} = -6.444\ldots \)
The list is ordered from least to greatest:
\[
-7 < -6.6 < \text{blank} < -6.444\ldots
\]
The blank must be a number between \(-6.6\) and \(-6.444\).
**Example Value:**
\[
-6.5
\]
### 2. **\(\text{blank}\), 8.75, \(8 \frac{4}{5}\), \(\sqrt{81}\)**
**Step-by-Step:**
- \( 8 \frac{4}{5} = 8.8 \)
- \( \sqrt{81} = 9 \)
The list is ordered from least to greatest:
\[
\text{blank} < 8.75 < 8.8 < 9
\]
The blank must be a number less than \(8.75\).
**Example Value:**
\[
8.5
\]
### 3. \(-2 \frac{9}{10}\), **,** \(-2 \frac{3}{5}\), \(-2.45\)
**Step-by-Step:**
- \(-2 \frac{9}{10} = -2.9\)
- \(-2 \frac{3}{5} = -2.6\)
The list is ordered from least to greatest:
\[
-2.9 < \text{blank} < -2.6 < -2.45
\]
The blank must be a number between \(-2.9\) and \(-2.6\).
**Example Value:**
\[
-2.7
\]
### **Summary of Example Values:**
1. **\(-6.5\)**
2. **\(8.5\)**
3. **\(-2.7\)**
Reviewed and approved by the UpStudy tutoring team
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Extra Insights
For the first list, the missing number should be between \( -\sqrt{49} \) (which equals -7) and \( -6.\overline{4} \) (which is approximately -6.4). A suitable value is \( -7,5 \). In the second list, the missing number must fall between the empty spot and \( 8 \frac{4}{5} \) (which is equal to 8.8) and \( 8.75 \). A good candidate for this spot could be \( 8.5 \). For the third list, the missing number should be situated between \( -2 \frac{9}{10} \) (which is approximately -2.9) and \( -2 \frac{3}{5} \) (which is equal to -2.6). An example that fits is \( -2.8 \).