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

Absolutely! Let’s solve the worksheet step by step and explain each part clearly.

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## 📘 Part 1: Converting Fractions to Decimals

Example 1: Convert 1/10 to a decimal

- “1 out of 10” = 1 tenth → 0.1
- Explanation: The denominator is 10, so we write the numerator (1) in the tenths place → 0.1

Example 2: Convert 3/100 to a decimal

- “3 out of 100” = 3 hundredths → 0.03
- Explanation: Denominator is 100 → write numerator (3) in the hundredths place → 0.03

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## 📘 Part 2: Converting Decimals to Fractions

Example 1: Convert 0.8 to a fraction

- 0.8 = 8 tenths → 8/10
- We can simplify: 8 ÷ 2 / 10 ÷ 2 = 4/5 (but the worksheet shows 8/10 — both are correct; simplified form is often preferred)

Example 2: Convert 0.72 to a fraction

- 0.72 = 72 hundredths → 72/100
- Simplify: divide numerator and denominator by 4 → 18/25

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## ✍️ Section 1: Write each fraction as a decimal

Let’s convert each:

| Fraction | Decimal |
|----------|---------|
| 1/10 | 0.1 (1 tenth) |
| 9/10 | 0.9 (9 tenths) |
| 40/100 | 0.40 or 0.4 (40 hundredths = 4 tenths) |
| 5/100 | 0.05 (5 hundredths) |
| 7/10 | 0.7 (7 tenths) |
| 80/100 | 0.80 or 0.8 (80 hundredths = 8 tenths) |
| 6/10 | 0.6 (6 tenths) |
| 90/100 | 0.90 or 0.9 (90 hundredths = 9 tenths) |
| 2/100 | 0.02 (2 hundredths) |
| 30/100 | 0.30 or 0.3 (30 hundredths = 3 tenths) |

✔ Note: You can drop trailing zeros after the decimal if they’re at the end (e.g., 0.40 = 0.4), but it’s fine to leave them for clarity.

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## ✍️ Section 2: Write each decimal as a fraction

We’ll write each as a fraction over 10 or 100, then simplify if possible.

| Decimal | Fraction (unsimplified) | Simplified Fraction |
|---------|--------------------------|----------------------|
| 0.4 | 4/10 | 2/5 |
| 0.11 | 11/100 | 11/100 (already simplest) |
| 0.9 | 9/10 | 9/10 |
| 0.67 | 67/100 | 67/100 |
| 0.91 | 91/100 | 91/100 |
| 0.2 | 2/10 | 1/5 |
| 0.55 | 55/100 | 11/20 |
| 0.23 | 23/100 | 23/100 |
| 0.3 | 3/10 | 3/10 |
| 0.52 | 52/100 | 13/25 |
| 0.19 | 19/100 | 19/100 |
| 0.08 | 8/100 | 2/25 |

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## 🔍 How to Simplify Fractions:
To simplify, find the Greatest Common Divisor (GCD) of numerator and denominator.

Examples:
- 4/10 → GCD of 4 and 10 is 2 → 4÷2 / 10÷2 = 2/5
- 55/100 → GCD of 55 and 100 is 5 → 55÷5 / 100÷5 = 11/20
- 52/100 → GCD of 52 and 100 is 4 → 52÷4 / 100÷4 = 13/25

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## ✔ Final Answers Summary:

Section 1: Fractions → Decimals

1. 0.1
2. 0.9
3. 0.4
4. 0.05
5. 0.7
6. 0.8
7. 0.6
8. 0.9
9. 0.02
10. 0.3

Section 2: Decimals → Fractions (Simplified)

1. 2/5
2. 11/100
3. 9/10
4. 67/100
5. 91/100
6. 1/5
7. 11/20
8. 23/100
9. 3/10
10. 13/25
11. 19/100
12. 2/25

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💡 Tip: Always check if your fraction can be simplified! It makes your answer cleaner and more precise.

Let me know if you’d like this turned into a printable answer sheet or need help with visual aids! 😊