Decimals, fractions, and percentages worksheet with conversion and comparison exercises.

Let’s solve each part step by step.

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Part 1: Complete the table

We need to convert between decimals, fractions, and percentages.

Remember:
- To turn a decimal into a fraction: write it over 100 (if two decimal places), then simplify if needed.
- To turn a decimal into a percentage: multiply by 100 and add %.
- To turn a fraction into a decimal: divide numerator by denominator.
- To turn a fraction into a percentage: first turn to decimal, then ×100.
- To turn a percentage into a decimal: divide by 100.
- To turn a percentage into a fraction: write over 100, then simplify.

Let’s fill in row by row:

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

Row 2: Decimal = 0.32
- Fraction: 0.32 = 32/100 = 8/25 (divide top and bottom by 4)
- Percentage: 0.32 × 100 = 32%

Row 3: Fraction = 23/100
- Decimal: 23 ÷ 100 = 0.23
- Percentage: 0.23 × 100 = 23%

Row 4: Fraction = 7/100
- Decimal: 7 ÷ 100 = 0.07
- Percentage: 0.07 × 100 = 7%

Row 5: Percentage = 41%
- Decimal: 41 ÷ 100 = 0.41
- Fraction: 41/100 → already simplified → 41/100

Row 6: Percentage = 8%
- Decimal: 8 ÷ 100 = 0.08
- Fraction: 8/100 = 2/25 (divide top and bottom by 4)

So 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’ll convert all to decimals to compare easily.

Set 1: 7/100, 12%, 0.09
- 7/100 = 0.07
- 12% = 0.12
- 0.09 = 0.09

Order from smallest: 0.07, 0.09, 0.12 → so:
7/100, 0.09, 12%

Set 2: 23/100, 3%, 0.3
- 23/100 = 0.23
- 3% = 0.03
- 0.3 = 0.30

Order: 0.03, 0.23, 0.30 → so:
3%, 23/100, 0.3

Set 3: 9/100, 10%, 0.01
- 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 =)

Convert both sides to same form (decimals easiest).

4. 0.77 ___ 70%
- 70% = 0.70
- 0.77 > 0.70 → >

5. 30% ___ 3/100
- 30% = 0.30
- 3/100 = 0.03
- 0.30 > 0.03 → >

6. 42/100 ___ 0.3
- 42/100 = 0.42
- 0.3 = 0.30
- 0.42 > 0.30 → >

7. 0.62 ___ 7%
- 7% = 0.07
- 0.62 > 0.07 → >

8. 29% ___ 35/100
- 29% = 0.29
- 35/100 = 0.35
- 0.29 < 0.35 → <

9. 35/100 ___ 0.4
- 35/100 = 0.35
- 0.4 = 0.40
- 0.35 < 0.40 → <

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Final Answer:

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% |

Ordering:

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

Comparison signs:

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