Math worksheet: Convert repeating decimals to fractions and color the dinosaur image.

Absolutely! Let’s solve this “Repeating Decimals to Fractions” coloring activity step by step.

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## 🎯 GOAL:
Convert the repeating decimals into simplified fractions, then use the key to color the sections of the mystery picture accordingly.

We have 3 problems:

1. 0.54̅ (which means 0.5444...)
2. 0.16̅ (which means 0.1666...)
3. 0.183̅ (which means 0.18333...)

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## 🔢 STEP 1: Convert Repeating Decimals to Fractions

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✔ Problem 1: Convert 0.54̅ = 0.5444...

Let \( x = 0.5444... \)

Multiply both sides by 10 to move the decimal past the non-repeating part:
→ \( 10x = 5.444... \)

Now multiply by 100 to move the decimal past the repeating part:
→ \( 100x = 54.444... \)

Subtract the first equation from the second:

\[
\begin{align*}
100x &= 54.444... \\
- 10x &= 5.444... \\
\hline
90x &= 49 \\
x &= \frac{49}{90}
\end{align*}
\]

✔ So, 0.54̅ = 49/90

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✔ Problem 2: Convert 0.16̅ = 0.1666...

Let \( x = 0.1666... \)

Multiply by 10 to get:
→ \( 10x = 1.666... \)

Multiply by 100 to get:
→ \( 100x = 16.666... \)

Subtract:

\[
\begin{align*}
100x &= 16.666... \\
- 10x &= 1.666... \\
\hline
90x &= 15 \\
x &= \frac{15}{90} = \frac{1}{6}
\end{align*}
\]

✔ So, 0.16̅ = 1/6

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✔ Problem 3: Convert 0.183̅ = 0.18333...

Let \( x = 0.18333... \)

Multiply by 100 to move past the non-repeating “18”:
→ \( 100x = 18.333... \)

Multiply by 1000 to move past the repeating “3”:
→ \( 1000x = 183.333... \)

Subtract:

\[
\begin{align*}
1000x &= 183.333... \\
- 100x &= 18.333... \\
\hline
900x &= 165 \\
x &= \frac{165}{900}
\end{align*}
\]

Simplify: divide numerator and denominator by 15 →
\( \frac{165 ÷ 15}{900 ÷ 15} = \frac{11}{60} \)

✔ So, 0.183̅ = 11/60

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## 🖍️ STEP 2: Use the Coloring Key

Here’s the key from the image:

| Color | Fraction |
|-----------|----------------|
| Red | 1/6 |
| Orange | 11/60 |
| Green | 49/90 |
| Purple | ? |
| Brown | ? |
| Yellow | ? |
| Light Blue| ? |
| Blue | ? |
| Pink | ? |

From our answers:

- Problem 1: 49/90 → Green
- Problem 2: 1/6 → Red
- Problem 3: 11/60 → Orange

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## 🧩 STEP 3: Apply to the Coloring Sheet

In the uncolored image on the right, each region is labeled with a fraction.

You must find all regions labeled:

- 49/90 → Color them Green
- 1/6 → Color them Red
- 11/60 → Color them Orange

*(Note: The other colors like Purple, Brown, etc., likely correspond to other fractions not in these 3 problems — perhaps from other versions or additional problems not shown here. But since only these 3 are given, we focus on them.)*

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## 🎨 FINAL ANSWER:

✔ Coloring Instructions Based on Your 3 Problems:

- All sections labeled 49/90 → Green
- All sections labeled 1/6 → Red
- All sections labeled 11/60 → Orange

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## 💡 BONUS TIP:

The colored example on the left shows a dinosaur or dragon-like creature — so after coloring correctly, you’ll reveal that image!

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✔ Summary of Solutions:

| Decimal | Fraction | Color |
|-------------|----------|--------|
| 0.54̅ | 49/90 | Green |
| 0.16̅ | 1/6 | Red |
| 0.183̅ | 11/60 | Orange |

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Let me know if you’d like help coloring the actual sheet or solving more problems! 😊