Converting Fractions, Decimals, and Percents (B) Worksheet | PDF ... - Free Printable

Let's solve this step-by-step by filling in the missing values in each table. We'll convert between fractions, decimals, and percentages using standard conversion methods:

---

🔁 Conversion Rules:

- Decimal → Percentage: Multiply by 100 and add %
- Percentage → Decimal: Divide by 100
- Fraction → Decimal: Divide numerator by denominator
- Decimal → Fraction: Write as a fraction over 10, 100, etc., then simplify
- Fraction → Percentage: Convert to decimal first, then multiply by 100

---

## ✔ Table 1: Decimal ↔ Percentage

| Decimal | 0.01 | 0.58 | 0.09 | | | | |
|--------|------|------|------|-----|-----|-----|-----|
| Percentage | | | | 6% | 0.2% | 1.5% | ½% |

Step-by-step:

1. 0.01 → %
$ 0.01 \times 100 = 1\% $

2. 0.58 → %
$ 0.58 \times 100 = 58\% $

3. 0.09 → %
$ 0.09 \times 100 = 9\% $

4. 6% → Decimal
$ 6 \div 100 = 0.06 $

5. 0.2% → Decimal
$ 0.2 \div 100 = 0.002 $

6. 1.5% → Decimal
$ 1.5 \div 100 = 0.015 $

7. ½% → Decimal
$ \frac{1}{2} \% = 0.5\% $ → $ 0.5 \div 100 = 0.005 $

✔ Completed Table 1:

| Decimal | 0.01 | 0.58 | 0.09 | 0.06 | 0.002 | 0.015 | 0.005 |
|--------|------|------|------|------|-------|-------|-------|
| Percentage | 1% | 58% | 9% | 6% | 0.2% | 1.5% | ½% |

---

## ✔ Table 2: Fraction ↔ Percentage

| Fraction | ¼ | ⅒ | ³⁄₁₀₀ | | | | |
|---------|----|----|--------|-----|-----|-----|-----|
| Percentage | | | | 50% | 17% | 90% | 1% |

Step-by-step:

1. ¼ → %
$ \frac{1}{4} = 0.25 \rightarrow 0.25 \times 100 = 25\% $

2. ⅒ → %
$ \frac{1}{10} = 0.1 \rightarrow 10\% $

3. ³⁄₁₀₀ → %
$ \frac{3}{100} = 0.03 \rightarrow 3\% $

4. 50% → Fraction
$ 50\% = \frac{50}{100} = \frac{1}{2} $

5. 17% → Fraction
$ \frac{17}{100} $ (already simplified)

6. 90% → Fraction
$ \frac{90}{100} = \frac{9}{10} $

7. 1% → Fraction
$ \frac{1}{100} $

✔ Completed Table 2:

| Fraction | ¼ | ⅒ | ³⁄₁₀₀ | ½ | ¹⁷⁄₁₀₀ | ⁹⁄₁₀ | ¹⁄₁₀₀ |
|---------|----|----|--------|-----|--------|-------|--------|
| Percentage | 25% | 10% | 3% | 50% | 17% | 90% | 1% |

---

## ✔ Table 3: Fraction ↔ Percentage

| Fraction | | | | ³⁄₅ | ¹⁄₅₀ | ¹²⁄₂₅ | ⁷⁄₂₀ |
|---------|-----|-----|-----|-----|------|--------|-------|
| Percentage | 20% | 80% | 15% | | | | |

Step-by-step:

1. 20% → Fraction
$ \frac{20}{100} = \frac{1}{5} $

2. 80% → Fraction
$ \frac{80}{100} = \frac{4}{5} $

3. 15% → Fraction
$ \frac{15}{100} = \frac{3}{20} $

4. ³⁄₅ → %
$ \frac{3}{5} = 0.6 \rightarrow 60\% $

5. ¹⁄₅₀ → %
$ \frac{1}{50} = 0.02 \rightarrow 2\% $

6. ¹²⁄₂₅ → %
$ \frac{12}{25} = 0.48 \rightarrow 48\% $

7. ⁷⁄₂₀ → %
$ \frac{7}{20} = 0.35 \rightarrow 35\% $

✔ Completed Table 3:

| Fraction | ¹⁄₅ | ⁴⁄₅ | ³⁄₂₀ | ³⁄₅ | ¹⁄₅₀ | ¹²⁄₂₅ | ⁷⁄₂₀ |
|---------|------|------|-------|-----|------|--------|-------|
| Percentage | 20% | 80% | 15% | 60% | 2% | 48% | 35% |

---

## ✔ Table 4: Fraction → Decimal

| Fraction | ¹⁄₃ | ²⁄₃ | ¹⁄₉ | ¹⁄₆ | ⁵⁄₆ | ¹⁄₁₁ | ³⁄₇ |
|---------|------|------|------|------|------|------|------|
| Decimal | | | | | | | |

We’ll convert each fraction to decimal using division.

1. ¹⁄₃
$ 1 \div 3 = 0.\overline{3} \approx 0.333 $

2. ²⁄₃
$ 2 \div 3 = 0.\overline{6} \approx 0.667 $

3. ¹⁄₉
$ 1 \div 9 = 0.\overline{1} \approx 0.111 $

4. ¹⁄₆
$ 1 \div 6 = 0.1\overline{6} \approx 0.167 $

5. ⁵⁄₆
$ 5 \div 6 = 0.8\overline{3} \approx 0.833 $

6. ¹⁄₁₁
$ 1 \div 11 = 0.\overline{09} \approx 0.0909 $

7. ³⁄₇
$ 3 \div 7 \approx 0.4286 $

✔ Completed Table 4:

| Fraction | ¹⁄₃ | ²⁄₃ | ¹⁄₉ | ¹⁄₆ | ⁵⁄₆ | ¹⁄₁₁ | ³⁄₇ |
|---------|------|------|------|------|------|------|------|
| Decimal | 0.333... | 0.666... | 0.111... | 0.166... | 0.833... | 0.0909... | 0.4286... |

> Note: These are repeating decimals. You can write them as:
> - $ \frac{1}{3} = 0.\overline{3} $
> - $ \frac{2}{3} = 0.\overline{6} $
> - $ \frac{1}{9} = 0.\overline{1} $
> - $ \frac{1}{6} = 0.1\overline{6} $
> - $ \frac{5}{6} = 0.8\overline{3} $
> - $ \frac{1}{11} = 0.\overline{09} $
> - $ \frac{3}{7} \approx 0.4286 $ (repeats every 6 digits: 0.428571...)

---

🟩 Final Answer Summary:

#### Table 1: Decimal ↔ Percentage
| Decimal | 0.01 | 0.58 | 0.09 | 0.06 | 0.002 | 0.015 | 0.005 |
|--------|------|------|------|------|-------|-------|-------|
| Percentage | 1% | 58% | 9% | 6% | 0.2% | 1.5% | ½% |

#### Table 2: Fraction ↔ Percentage
| Fraction | ¼ | ⅒ | ³⁄₁₀₀ | ½ | ¹⁷⁄₁₀₀ | ⁹⁄₁₀ | ¹⁄₁₀₀ |
|---------|----|----|--------|-----|--------|-------|--------|
| Percentage | 25% | 10% | 3% | 50% | 17% | 90% | 1% |

#### Table 3: Fraction ↔ Percentage
| Fraction | ¹⁄₅ | ⁴⁄₅ | ³⁄₂₀ | ³⁄₅ | ¹⁄₅₀ | ¹²⁄₂₅ | ⁷⁄₂₀ |
|---------|------|------|-------|-----|------|--------|-------|
| Percentage | 20% | 80% | 15% | 60% | 2% | 48% | 35% |

#### Table 4: Fraction → Decimal
| Fraction | ¹⁄₃ | ²⁄₃ | ¹⁄₉ | ¹⁄₆ | ⁵⁄₆ | ¹⁄₁₁ | ³⁄₇ |
|---------|------|------|------|------|------|------|------|
| Decimal | 0.333... | 0.666... | 0.111... | 0.166... | 0.833... | 0.0909... | 0.4286... |

---

Let me know if you'd like this formatted as a printable sheet or need explanations for any specific conversions!