Answer key showing solutions for converting fractions to decimals, including examples of repeating decimals marked with dots above the last digit.

It looks like you've uploaded an image of a completed worksheet titled *"Converting Fractions to Decimals Answers"*, which already contains the correct decimal equivalents for each fraction. However, since you're asking me to solve the problem and explain the solution, I’ll go through the process of how to convert each fraction to a decimal, with explanations — especially focusing on the ones that have repeating decimals (as noted in the instructions).

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🔢 How to Convert Fractions to Decimals

To convert a fraction to a decimal:
- Divide the numerator by the denominator.
- If the division results in a repeating decimal, we use a dot above the last digit to indicate repetition.

Let’s walk through each problem step-by-step:

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1) $ \frac{1}{5} = 0.2 $

- $ 1 ÷ 5 = 0.2 $

✔ Simple division: 5 goes into 10 two times → 0.2

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2) $ \frac{3}{12} = 0.25 $

- Simplify first: $ \frac{3}{12} = \frac{1}{4} $
- $ 1 ÷ 4 = 0.25 $

✔ Known fact: $ \frac{1}{4} = 0.25 $

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3) $ \frac{3}{8} = 0.375 $

- $ 3 ÷ 8 = 0.375 $

✔ Long division:
8 into 3.000 → 0.375

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4) $ \frac{4}{5} = 0.8 $

- $ 4 ÷ 5 = 0.8 $

✔ Or think: $ \frac{4}{5} = \frac{8}{10} = 0.8 $

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5) $ \frac{7}{4} = 1.75 $

- $ 7 ÷ 4 = 1.75 $

✔ 4 goes into 7 once (remainder 3), then 30 ÷ 4 = 7.5 → 1.75

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6) $ \frac{7}{16} = 0.4375 $

- $ 7 ÷ 16 = 0.4375 $

✔ Long division: 16 into 7.0000 → 0.4375

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7) $ \frac{1}{6} = 0.\overline{16} $ → written as 0.166... (with dot over 6)

- $ 1 ÷ 6 = 0.1666... $

✔ Division:
6 into 1.0000 →
- 6 × 0.1 = 0.6 → remainder 0.4
- 0.40 ÷ 6 = 0.06 → remainder 0.04
- 0.040 ÷ 6 = 0.006 → remainder 0.004
→ Repeats forever: 0.1666...

So, 0.16̅ (dot over 6) means 6 repeats infinitely.

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8) $ \frac{11}{2} = 5.5 $

- $ 11 ÷ 2 = 5.5 $

✔ 2 × 5 = 10, remainder 1 → 1/2 = 0.5 → total = 5.5

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9) $ \frac{18}{8} = 2.25 $

- Simplify: $ \frac{18}{8} = \frac{9}{4} $
- $ 9 ÷ 4 = 2.25 $

✔ Or: 4 × 2 = 8, remainder 1 → 1/4 = 0.25 → 2.25

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10) $ \frac{6}{15} = 0.4 $

- Simplify: $ \frac{6}{15} = \frac{2}{5} $
- $ 2 ÷ 5 = 0.4 $

✔ Or: $ \frac{2}{5} = \frac{4}{10} = 0.4 $

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11) $ \frac{7}{3} = 2.\overline{3} $ → 2.333...

- $ 7 ÷ 3 = 2.333... $

✔ Division:
3 × 2 = 6, remainder 1 → 1.0 ÷ 3 = 0.333...
So: 2 + 0.333... = 2.333...

The dot over 3 indicates infinite repetition.

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12) $ \frac{6}{20} = 0.3 $

- Simplify: $ \frac{6}{20} = \frac{3}{10} $
- $ 3 ÷ 10 = 0.3 $

✔ Easy: 3 tenths = 0.3

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13) $ \frac{9}{15} = 0.6 $

- Simplify: $ \frac{9}{15} = \frac{3}{5} $
- $ 3 ÷ 5 = 0.6 $

✔ Or: $ \frac{3}{5} = \frac{6}{10} = 0.6 $

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14) $ \frac{16}{6} = 2.\overline{6} $ → 2.666...

- Simplify: $ \frac{16}{6} = \frac{8}{3} $
- $ 8 ÷ 3 = 2.666... $

✔ 3 × 2 = 6, remainder 2 → 2.0 ÷ 3 = 0.666... → so 2.666...

Dot over 6 shows it repeats.

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15) $ \frac{7}{9} = 0.\overline{7} $ → 0.777...

- $ 7 ÷ 9 = 0.777... $

✔ Long division:
9 into 7.000 → 0.777...
Each time: 9 × 0.7 = 6.3 → remainder 0.7 → repeats.

So: 0.7̅ (dot over 7)

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16) $ \frac{9}{5} = 1.8 $

- $ 9 ÷ 5 = 1.8 $

✔ 5 × 1 = 5, remainder 4 → 4/5 = 0.8 → 1.8

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✔ Summary of Key Concepts:

| Fraction | Decimal | Notes |
|--------|--------|-------|
| $ \frac{1}{6} $ | $ 0.1\overline{6} $ | 6 repeats |
| $ \frac{7}{3} $ | $ 2.\overline{3} $ | 3 repeats |
| $ \frac{16}{6} = \frac{8}{3} $ | $ 2.\overline{6} $ | 6 repeats |
| $ \frac{7}{9} $ | $ 0.\overline{7} $ | 7 repeats |

> 🔁 Repeating decimals happen when the denominator has prime factors other than 2 or 5 (like 3, 7, 9, etc.).

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📌 Final Answer Check:

All answers on your sheet are correct, including the notation for repeating decimals.

You can verify any result using long division or a calculator.

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Let me know if you'd like a printable version, visual explanation, or practice problems!