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Answer :
Sure, let's look at how to order the given numbers from smallest to largest. The numbers we have are:
1. [tex]\(-0 . \overline{6}\)[/tex]
2. [tex]\(\sqrt{14}\)[/tex]
3. [tex]\(3.85\)[/tex]
4. [tex]\(-\frac{34}{50}\)[/tex]
### Step-by-Step Solution:
1. Convert each number into a common form for easy comparison:
- [tex]\(-0 . \overline{6}\)[/tex]: This is a repeating decimal, which is approximately [tex]\(-0.6666\)[/tex].
- [tex]\(\sqrt{14}\)[/tex]: Using a calculator, [tex]\(\sqrt{14}\)[/tex] is approximately [tex]\(3.7417\)[/tex].
- [tex]\(3.85\)[/tex]: This is already in decimal form.
- [tex]\(-\frac{34}{50}\)[/tex]: Simplify the fraction: [tex]\(-\frac{34}{50}\)[/tex] = [tex]\(-0.68\)[/tex].
2. List the approximate decimal values:
- [tex]\(-0.6666\)[/tex]
- [tex]\(3.7417\)[/tex]
- [tex]\(3.85\)[/tex]
- [tex]\(-0.68\)[/tex]
3. Order these values from smallest to largest:
- The smallest value is [tex]\(-0.68\)[/tex].
- Next is [tex]\(-0.6666\)[/tex].
- After that is [tex]\(3.7417\)[/tex] ([tex]\(\sqrt{14}\)[/tex]).
- The largest value is [tex]\(3.85\)[/tex].
### Ordered Numbers:
- [tex]\(-0.68\)[/tex]
- [tex]\(-0.6666\)[/tex]
- [tex]\(3.7417\)[/tex] ([tex]\(\sqrt{14}\)[/tex])
- [tex]\(3.85\)[/tex]
Thus, the numbers in order from smallest to largest are:
[tex]\[
-\frac{34}{50}, -0 . \overline{6}, \sqrt{14}, 3.85
\][/tex]
1. [tex]\(-0 . \overline{6}\)[/tex]
2. [tex]\(\sqrt{14}\)[/tex]
3. [tex]\(3.85\)[/tex]
4. [tex]\(-\frac{34}{50}\)[/tex]
### Step-by-Step Solution:
1. Convert each number into a common form for easy comparison:
- [tex]\(-0 . \overline{6}\)[/tex]: This is a repeating decimal, which is approximately [tex]\(-0.6666\)[/tex].
- [tex]\(\sqrt{14}\)[/tex]: Using a calculator, [tex]\(\sqrt{14}\)[/tex] is approximately [tex]\(3.7417\)[/tex].
- [tex]\(3.85\)[/tex]: This is already in decimal form.
- [tex]\(-\frac{34}{50}\)[/tex]: Simplify the fraction: [tex]\(-\frac{34}{50}\)[/tex] = [tex]\(-0.68\)[/tex].
2. List the approximate decimal values:
- [tex]\(-0.6666\)[/tex]
- [tex]\(3.7417\)[/tex]
- [tex]\(3.85\)[/tex]
- [tex]\(-0.68\)[/tex]
3. Order these values from smallest to largest:
- The smallest value is [tex]\(-0.68\)[/tex].
- Next is [tex]\(-0.6666\)[/tex].
- After that is [tex]\(3.7417\)[/tex] ([tex]\(\sqrt{14}\)[/tex]).
- The largest value is [tex]\(3.85\)[/tex].
### Ordered Numbers:
- [tex]\(-0.68\)[/tex]
- [tex]\(-0.6666\)[/tex]
- [tex]\(3.7417\)[/tex] ([tex]\(\sqrt{14}\)[/tex])
- [tex]\(3.85\)[/tex]
Thus, the numbers in order from smallest to largest are:
[tex]\[
-\frac{34}{50}, -0 . \overline{6}, \sqrt{14}, 3.85
\][/tex]
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