Fraction Basics: Converting Fractions and Decimals | Worksheet ... - Free Printable

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🔹 Section 1: Examples

#### ✔ Converting Fractions to Decimals
- Example 1: Convert \( \frac{1}{10} \) to a decimal
→ \( \frac{1}{10} = 0.1 \)
*Explanation:* One tenth means 1 divided by 10 = 0.1

- Example 2: Convert \( \frac{50}{100} \) to a decimal
→ \( \frac{50}{100} = 0.50 \) or simply \( 0.5 \)
*Explanation:* Fifty hundredths = 50 ÷ 100 = 0.5

#### ✔ Converting Decimals to Fractions
- Example 3: Convert 0.8 to a fraction
→ \( 0.8 = \frac{8}{10} = \frac{4}{5} \)
*Explanation:* 0.8 = 8 tenths = \( \frac{8}{10} \), simplify by dividing numerator and denominator by 2 → \( \frac{4}{5} \)

- Example 4: Convert 0.72 to a fraction
→ \( 0.72 = \frac{72}{100} = \frac{18}{25} \)
*Explanation:* 72 hundredths = \( \frac{72}{100} \), divide numerator and denominator by 4 → \( \frac{18}{25} \)

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🔹 Section 2: Practice Problems

#### 🟦 Write each fraction as a decimal

Let’s go through each one:

1. \( \frac{1}{10} = 0.1 \)
2. \( \frac{3}{10} = 0.3 \)
3. \( \frac{7}{10} = 0.7 \)
4. \( \frac{9}{10} = 0.9 \)
5. \( \frac{1}{100} = 0.01 \)
6. \( \frac{25}{100} = 0.25 \)
7. \( \frac{50}{100} = 0.50 \)
8. \( \frac{75}{100} = 0.75 \)
9. \( \frac{99}{100} = 0.99 \)
10. \( \frac{1}{2} = 0.5 \) *(Note: This is equivalent to \( \frac{50}{100} \))*

> ✔ Tip: For denominators of 10 or 100, just move the decimal point:
> - \( \frac{a}{10} = a \div 10 \) → place decimal one spot left
> - \( \frac{a}{100} = a \div 100 \) → two spots left

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#### 🟨 Write each decimal as a fraction

Now convert decimals to fractions and simplify if possible.

1. \( 0.4 = \frac{4}{10} = \frac{2}{5} \)
2. \( 0.11 = \frac{11}{100} \) *(already simplified)*
3. \( 0.9 = \frac{9}{10} \)
4. \( 0.05 = \frac{5}{100} = \frac{1}{20} \)
5. \( 0.23 = \frac{23}{100} \)
6. \( 0.91 = \frac{91}{100} \)
7. \( 0.2 = \frac{2}{10} = \frac{1}{5} \)
8. \( 0.55 = \frac{55}{100} = \frac{11}{20} \)
9. \( 0.3 = \frac{3}{10} \)
10. \( 0.52 = \frac{52}{100} = \frac{13}{25} \)
11. \( 0.19 = \frac{19}{100} \)
12. \( 0.08 = \frac{8}{100} = \frac{2}{25} \)

> ✔ Tip: Write the decimal as a fraction over 10, 100, or 1000 depending on decimal places, then simplify.

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✔ Summary of Key Rules:

| Rule | Example |
|------|--------|
| Fraction → Decimal | Divide numerator by denominator |
| Decimal → Fraction | Write decimal as fraction with denominator 10, 100, etc., then simplify |
| Simplify fractions | Use GCF (Greatest Common Factor) |

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✔ Final Answer Table

#### Fractions to Decimals:
1. 0.1
2. 0.3
3. 0.7
4. 0.9
5. 0.01
6. 0.25
7. 0.50
8. 0.75
9. 0.99
10. 0.5

#### Decimals to Fractions:
1. \( \frac{2}{5} \)
2. \( \frac{11}{100} \)
3. \( \frac{9}{10} \)
4. \( \frac{1}{20} \)
5. \( \frac{23}{100} \)
6. \( \frac{91}{100} \)
7. \( \frac{1}{5} \)
8. \( \frac{11}{20} \)
9. \( \frac{3}{10} \)
10. \( \frac{13}{25} \)
11. \( \frac{19}{100} \)
12. \( \frac{2}{25} \)

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