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

Let's solve the worksheet step by step.

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Part 1: Complete the table

We need to convert between decimals, fractions, and percentages. Remember:
- To convert a decimal to a fraction: write it over 100 (if two decimal places) and simplify.
- To convert a decimal to a percentage: multiply by 100.
- To convert a fraction to a decimal: divide numerator by denominator.
- To convert a fraction to a percentage: divide and multiply by 100.

#### Row 1: Decimal = 0.05
- Fraction: $ \frac{5}{100} = \frac{1}{20} $
- Percentage: $ 0.05 \times 100 = 5\% $

#### Row 2: Decimal = 0.32
- Fraction: $ \frac{32}{100} = \frac{8}{25} $
- Percentage: $ 0.32 \times 100 = 32\% $

#### Row 3: Fraction = $ \frac{23}{100} $
- Decimal: $ 23 \div 100 = 0.23 $
- Percentage: $ 23\% $

#### Row 4: Fraction = $ \frac{7}{100} $
- Decimal: $ 7 \div 100 = 0.07 $
- Percentage: $ 7\% $

#### Row 5: Percentage = 41%
- Decimal: $ 41 \div 100 = 0.41 $
- Fraction: $ \frac{41}{100} $ (already simplified)

#### Row 6: Percentage = 8%
- Decimal: $ 8 \div 100 = 0.08 $
- Fraction: $ \frac{8}{100} = \frac{2}{25} $

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✔ Completed Table:

| Decimal | Fraction | Percentage |
|--------|--------------|------------|
| 0.05 | $ \frac{1}{20} $ | 5% |
| 0.32 | $ \frac{8}{25} $ | 32% |
| 0.23 | $ \frac{23}{100} $ | 23% |
| 0.07 | $ \frac{7}{100} $ | 7% |
| 0.41 | $ \frac{41}{100} $ | 41% |
| 0.08 | $ \frac{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 values to the same form (e.g., decimals) for easy comparison.

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#### 1. $ \frac{7}{10},\ 12\%,\ 0.09 $

Convert to decimals:
- $ \frac{7}{10} = 0.7 $
- $ 12\% = 0.12 $
- $ 0.09 = 0.09 $

Order: $ 0.09,\ 0.12,\ 0.7 $

So: 0.09, 12%, $ \frac{7}{10} $

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#### 2. $ \frac{23}{100},\ 3\%,\ 0.3 $

Convert:
- $ \frac{23}{100} = 0.23 $
- $ 3\% = 0.03 $
- $ 0.3 = 0.3 $

Order: $ 0.03,\ 0.23,\ 0.3 $

So: 3%, $ \frac{23}{100} $, 0.3

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#### 3. $ \frac{9}{10},\ 10\%,\ 0.01 $

Convert:
- $ \frac{9}{10} = 0.9 $
- $ 10\% = 0.1 $
- $ 0.01 = 0.01 $

Order: $ 0.01,\ 0.1,\ 0.9 $

So: 0.01, 10%, $ \frac{9}{10} $

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✔ Answers for ordering:

1. 0.09, 12%, $ \frac{7}{10} $
2. 3%, $ \frac{23}{100} $, 0.3
3. 0.01, 10%, $ \frac{9}{10} $

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Part 3: Put in the correct sign (<, >, or =)

Compare each pair.

#### 4. 0.77 ○ 70%
- $ 70\% = 0.70 $
- $ 0.77 > 0.70 $
✔ >

#### 5. 30% ○ $ \frac{3}{100} $
- $ 30\% = 0.30 $
- $ \frac{3}{100} = 0.03 $
- $ 0.30 > 0.03 $
✔ >

#### 6. $ \frac{42}{100} $ ○ 0.3
- $ \frac{42}{100} = 0.42 $
- $ 0.42 > 0.3 $
✔ >

#### 7. 0.62 ○ 7%
- $ 7\% = 0.07 $
- $ 0.62 > 0.07 $
✔ >

#### 8. 29% ○ $ \frac{25}{100} $
- $ 29\% = 0.29 $
- $ \frac{25}{100} = 0.25 $
- $ 0.29 > 0.25 $
✔ >

#### 9. $ \frac{35}{100} $ ○ 0.4
- $ \frac{35}{100} = 0.35 $
- $ 0.35 < 0.4 $
✔ <

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✔ Final answers for comparisons:

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

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✔ Final Answer Summary:

#### Table:

| Decimal | Fraction | Percentage |
|--------|--------------|------------|
| 0.05 | $ \frac{1}{20} $ | 5% |
| 0.32 | $ \frac{8}{25} $ | 32% |
| 0.23 | $ \frac{23}{100} $ | 23% |
| 0.07 | $ \frac{7}{100} $ | 7% |
| 0.41 | $ \frac{41}{100} $ | 41% |
| 0.08 | $ \frac{2}{25} $ | 8% |

#### Ordering:
1. 0.09, 12%, $ \frac{7}{10} $
2. 3%, $ \frac{23}{100} $, 0.3
3. 0.01, 10%, $ \frac{9}{10} $

#### Comparisons:
4. >
5. >
6. >
7. >
8. >
9. <

Let me know if you'd like this formatted as a printable answer sheet!