Decimals, fractions and percentages - Fraction and Decimal ... - Free Printable

Let’s solve this 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 like x/100 into a decimal: just write as 0.xx
- To turn a fraction like x/100 into a percentage: it’s just x%
- To turn a percentage into a decimal: divide by 100
- To turn a percentage into a fraction: write over 100

Let’s fill in each 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 numerator and denominator by 4)
→ Percentage: 0.32 × 100 = 32%

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

Row 4: Fraction = 7/100
→ Decimal: 7 ÷ 100 = 0.07
→ Percentage: 7/100 = 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 by 4)

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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: 0.07 < 0.09 < 0.12 → 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 → 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 → 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. <