Math worksheet for converting decimals, fractions, and percentages.

Let’s solve this worksheet step by step. It covers decimals, fractions, and percentages, and how to convert between them.

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## 📊 PART 1: Complete the Table

We are given a table with some values filled in, and we need to fill in the missing ones using conversions.

Remember:
- To convert decimal → fraction: Write decimal over 100 (if 2 decimal places), then simplify.
- To convert decimal → percentage: Multiply by 100%.
- To convert fraction → decimal: Divide numerator by denominator.
- To convert fraction → percentage: Multiply fraction by 100%.
- To convert percentage → decimal: Divide by 100.
- To convert percentage → fraction: Write as /100, then simplify.

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Row 1: Decimal = 0.05

- Fraction: 0.05 = 5/100 = 1/20 (simplified)
- Percentage: 0.05 × 100% = 5%

✔ So:
Fraction = 1/20, Percentage = 5%

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Row 2: Decimal = 0.32

- Fraction: 0.32 = 32/100 = 8/25 (simplified)
- Percentage: 0.32 × 100% = 32%

✔ So:
Fraction = 8/25, Percentage = 32%

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Row 3: Fraction = 23/100

- Decimal: 23 ÷ 100 = 0.23
- Percentage: (23/100) × 100% = 23%

✔ So:
Decimal = 0.23, Percentage = 23%

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Row 4: Fraction = 7/100

- Decimal: 7 ÷ 100 = 0.07
- Percentage: (7/100) × 100% = 7%

✔ So:
Decimal = 0.07, Percentage = 7%

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Row 5: Percentage = 41%

- Decimal: 41 ÷ 100 = 0.41
- Fraction: 41/100 (already simplified)

✔ So:
Decimal = 0.41, Fraction = 41/100

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Row 6: Percentage = 8%

- Decimal: 8 ÷ 100 = 0.08
- Fraction: 8/100 = 2/25 (simplified)

✔ So:
Decimal = 0.08, Fraction = 2/25

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✔ Completed Table:

| Decimal | Fraction | Percentage |
|---------|----------|------------|
| 0.05 | 1/20 | 5% |
| 0.32 | 8/25 | 32% |
| 0.23 | 23/100 | 23% |
| 0.07 | 7/100 | 7% |
| 0.41 | 41/100 | 41% |
| 0.08 | 2/25 | 8% |

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## 🧮 PART 2: Rewrite each set of 3 in order, starting with the smallest

We need to convert all to the same form (e.g., decimals) to compare easily.

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Set 1: 7/100, 12%, 0.09

Convert all to decimals:

- 7/100 = 0.07
- 12% = 0.12
- 0.09 = 0.09

Order from smallest to largest:
0.07 < 0.09 < 0.12

So:
✔ 7/100, 0.09, 12%

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Set 2: 23/100, 3%, 0.3

Convert to decimals:

- 23/100 = 0.23
- 3% = 0.03
- 0.3 = 0.30

Order:
0.03 < 0.23 < 0.30

So:
✔ 3%, 23/100, 0.3

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Set 3: 9/100, 10%, 0.01

Convert to decimals:

- 9/100 = 0.09
- 10% = 0.10
- 0.01 = 0.01

Order:
0.01 < 0.09 < 0.10

So:
✔ 0.01, 9/100, 10%

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## ⚖️ PART 3: Put in correct sign (<, >, or =)

Again, convert everything to decimals for easy comparison.

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4. 0.77 ○ 70%

70% = 0.70
0.77 > 0.70 → >

✔ 0.77 > 70%

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5. 30% ○ 3/100

30% = 0.30
3/100 = 0.03
0.30 > 0.03 → >

✔ 30% > 3/100

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6. 42/100 ○ 0.3

42/100 = 0.42
0.42 > 0.3 → >

✔ 42/100 > 0.3

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7. 0.62 ○ 7%

7% = 0.07
0.62 > 0.07 → >

✔ 0.62 > 7%

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8. 29% ○ 35/100

29% = 0.29
35/100 = 0.35
0.29 < 0.35 → <

✔ 29% < 35/100

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9. 35/100 ○ 0.4

35/100 = 0.35
0.35 < 0.4 → <

✔ 35/100 < 0.4

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## ✔ FINAL ANSWERS:

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🔢 Table Completion:

| Decimal | Fraction | Percentage |
|---------|----------|------------|
| 0.05 | 1/20 | 5% |
| 0.32 | 8/25 | 32% |
| 0.23 | 23/100 | 23% |
| 0.07 | 7/100 | 7% |
| 0.41 | 41/100 | 41% |
| 0.08 | 2/25 | 8% |

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🔄 Ordering Sets:

1. 7/100, 0.09, 12%
2. 3%, 23/100, 0.3
3. 0.01, 9/100, 10%

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🔁 Comparison Signs:

4. >
5. >
6. >
7. >
8. <
9. <

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✔ All done! You now understand how to convert and compare decimals, fractions, and percentages. Great job!