I'll work through this step by step to convert between fractions, decimals, and percentages.
Row 1: 1/8
- Decimal: 1 ÷ 8 = 0.125
- Percentage: 0.125 × 100 = 12.5%
Row 2: 0.375 (decimal given)
- Fraction: 0.375 = 375/1000 = 3/8 (simplified)
- Percentage: 0.375 × 100 = 37.5%
Row 3: 33⅓% (percentage given)
- This is 33.333...% or 100/3 %
- As a fraction: 33⅓% = 100/3 ÷ 100 = 100/300 = 1/3
- As a decimal: 1 ÷ 3 = 0.333... = 0.̅3
Row 4: 0.̅6 (repeating decimal)
- Let x = 0.666...
- 10x = 6.666...
- 10x - x = 6.666... - 0.666...
- 9x = 6
- x = 6/9 = 2/3
- Percentage: 2/3 × 100 = 66.666...% = 66.̅6%
Row 5: 2.5% (percentage given)
- As a decimal: 2.5 ÷ 100 = 0.025
- As a fraction: 2.5/100 = 25/1000 = 1/40
Row 6: 0.005 (decimal given)
- As a fraction: 0.005 = 5/1000 = 1/200
- As a percentage: 0.005 × 100 = 0.5%
Row 7: 7/40
- Decimal: 7 ÷ 40 = 0.175
- Percentage: 0.175 × 100 = 17.5%
Row 8: 1/9
- Decimal: 1 ÷ 9 = 0.111... = 0.̅1
- Percentage: 1/9 × 100 = 11.111...% = 11.̅1%
Row 9: 1/7
- Decimal: 1 ÷ 7 = 0.142857142857... = 0.̅14̅2̅85̅7̅
- Percentage: 1/7 × 100 = 14.285714...% ≈ 14.2̅8̅57̅1̅4%
Row 10: 0.̅2 (repeating decimal)
- Let x = 0.222...
- 10x = 2.222...
- 10x - x = 2.222... - 0.222...
- 9x = 2
- x = 2/9
- Percentage: 2/9 × 100 = 22.222...% = 22.̅2%
Row 11: 77.̅7% (repeating percentage)
- 77.7% = 77.777...%
- As a decimal: 77.777... ÷ 100 = 0.777... = 0.̅7
- As a fraction: Let x = 0.777..., then 10x = 7.777..., so 9x = 7, x = 7/9
Row 12: 0.16 (repeating decimal - the 6 repeats)
- Let x = 0.1666...
- 10x = 1.666...
- 100x = 16.666...
- 100x - 10x = 16.666... - 1.666...
- 90x = 15
- x = 15/90 = 1/6
- Percentage: 1/6 × 100 = 16.666...% = 16.̅6%
Row 13: 25.̅5% (repeating percentage)
- 25.̅5% = 25.555...%
- As a decimal: 25.555... ÷ 100 = 0.2555...
- Let x = 0.2555...
- 10x = 2.555...
- 100x = 25.555...
- 100x - 10x = 25.555... - 2.555...
- 90x = 23
- x = 23/90
- As a fraction: 23/90
Final Answer:
| Fraction | Decimal | Percentage |
|----------|---------|------------|
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/3 | 0.̅3 | 33⅓% |
| 2/3 | 0.̅6 | 66.̅6% |
| 1/40 | 0.025 | 2.5% |
| 1/200 | 0.005 | 0.5% |
| 7/40 | 0.175 | 17.5% |
| 1/9 | 0.̅1 | 11.̅1% |
| 1/7 | 0.̅14̅2̅85̅7̅ | 14.̅2̅8̅57̅1̅4% |
| 2/9 | 0.̅2 | 22.̅2% |
| 7/9 | 0.̅7 | 77.7% |
| 1/6 | 0.1̅6 | 16.6% |
| 23/90 | 0.25̅5 | 25.̅5% |
Parent Tip: Review the logic above to help your child master the concept of fraction decimal percent table worksheet.
