Practice placing fractions, decimals, and square roots on a number line.

It looks like you're working on a math task involving ordering numbers on a number line. The goal is likely to compare and order the given numbers from least to greatest, then place them appropriately on the number line.

Let’s go step by step.

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🔢 Given Numbers:

1. $ 3\frac{1}{5} $
2. $ \frac{4}{9} $
3. $ 0.445 $
4. $ \sqrt{26} $
5. $ 5.\overline{1} $

We need to convert all of these into decimal form so we can compare them easily.

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✔ Step 1: Convert each number to decimal

#### 1. $ 3\frac{1}{5} $
This is a mixed number.
$$
3\frac{1}{5} = 3 + \frac{1}{5} = 3 + 0.2 = 3.2
$$

#### 2. $ \frac{4}{9} $
Divide 4 by 9:
$$
\frac{4}{9} \approx 0.444\ldots = 0.\overline{4}
$$

#### 3. $ 0.445 $
Already in decimal form → 0.445

#### 4. $ \sqrt{26} $
We know:
- $ \sqrt{25} = 5 $
- $ \sqrt{36} = 6 $
So $ \sqrt{26} $ is between 5 and 6.

Use approximation:
$$
\sqrt{26} \approx 5.1
$$
(Actually, more precisely: $ \sqrt{26} \approx 5.099 $)

#### 5. $ 5.\overline{1} $
This is a repeating decimal:
$$
5.\overline{1} = 5.1111\ldots
$$

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✔ Step 2: List all decimals

| Number | Decimal Form |
|-------|--------------|
| $ 3\frac{1}{5} $ | 3.2 |
| $ \frac{4}{9} $ | 0.444... |
| $ 0.445 $ | 0.445 |
| $ \sqrt{26} $ | ≈ 5.099 |
| $ 5.\overline{1} $ | 5.111... |

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✔ Step 3: Order from least to greatest

Now let's compare:

- $ \frac{4}{9} \approx 0.444\ldots $
- $ 0.445 $
- $ 3\frac{1}{5} = 3.2 $
- $ \sqrt{26} \approx 5.099 $
- $ 5.\overline{1} \approx 5.111\ldots $

So, ordered:
$$
\frac{4}{9} < 0.445 < 3\frac{1}{5} < \sqrt{26} < 5.\overline{1}
$$

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✔ Step 4: Place on the Number Line

You have a blank number line with tick marks. Let’s assume it goes from 0 to 6, with each tick representing 1 unit.

Here’s how to place them:

1. $ \frac{4}{9} \approx 0.444 $ → Just after 0, near 0.4
2. $ 0.445 $ → Very close to $ \frac{4}{9} $, slightly larger
3. $ 3\frac{1}{5} = 3.2 $ → Between 3 and 4, closer to 3
4. $ \sqrt{26} \approx 5.099 $ → Slightly less than 5.1
5. $ 5.\overline{1} = 5.111\ldots $ → Slightly more than 5.1

> 💡 Note: $ 0.444\ldots $ and $ 0.445 $ are very close — but $ 0.445 > 0.444\ldots $, since $ 0.445 = 0.4450 $, which is greater than $ 0.4444\ldots $

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✔ Final Answer (Ordered):

$$
\boxed{
\frac{4}{9} < 0.445 < 3\frac{1}{5} < \sqrt{26} < 5.\overline{1}
}
$$

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📝 Instructions for Your Notes:

Write this in your binder under “Number Line Practice” or “Comparing Real Numbers”:

> Task: Order the following numbers from least to greatest and plot on a number line:
>
> $ 3\frac{1}{5},\ \frac{4}{9},\ 0.445,\ \sqrt{26},\ 5.\overline{1} $
>
> Step-by-step:
> - Convert all to decimals:
> - $ 3\frac{1}{5} = 3.2 $
> - $ \frac{4}{9} \approx 0.444\ldots $
> - $ 0.445 $
> - $ \sqrt{26} \approx 5.099 $
> - $ 5.\overline{1} = 5.111\ldots $
>
> Order:
> $$
> \frac{4}{9} < 0.445 < 3\frac{1}{5} < \sqrt{26} < 5.\overline{1}
> $$
>
> Plotting on number line:
> - Start at 0, mark up to 6.
> - Place $ \frac{4}{9} $ and $ 0.445 $ just after 0.
> - Place $ 3.2 $ between 3 and 4.
> - Place $ \sqrt{26} $ just before 5.1.
> - Place $ 5.\overline{1} $ just after 5.1.

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✔ You’ve now practiced comparing rational and irrational numbers! Great job! 🎉