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Explanation:

Response
Part 1: Fraction to Decimal Conversion
  1. \( \frac{1}{8} \): Divide 1 by 8. \( 1 \div 8 = 0.125 \)
  2. \( \frac{1}{4} \): Divide 1 by 4. \( 1 \div 4 = 0.25 \)
  3. \( \frac{3}{8} \): Divide 3 by 8. \( 3 \div 8 = 0.375 \)
  4. \( \frac{1}{2} \): Divide 1 by 2. \( 1 \div 2 = 0.5 \)
  5. \( \frac{5}{8} \): Divide 5 by 8. \( 5 \div 8 = 0.625 \)
  6. \( \frac{3}{4} \): Divide 3 by 4. \( 3 \div 4 = 0.75 \)
  7. \( \frac{7}{8} \): Divide 7 by 8. \( 7 \div 8 = 0.875 \)
Part 2: Decimal to Fraction Conversion
  1. \( 0.062 \): \( 0.062 = \frac{62}{1000} = \frac{31}{500} \)
  2. \( 0.125 \): \( 0.125 = \frac{125}{1000} = \frac{1}{8} \)
  3. \( 0.312 \): \( 0.312 = \frac{312}{1000} = \frac{39}{125} \)
  4. \( 0.187 \): \( 0.187 = \frac{187}{1000} \) (since 187 and 1000 have no common factors other than 1)
  5. \( 0.750 \): \( 0.750 = \frac{750}{1000} = \frac{3}{4} \)
  6. \( 0.875 \): \( 0.875 = \frac{875}{1000} = \frac{7}{8} \)
  7. \( 0.937 \): \( 0.937 = \frac{937}{1000} \) (since 937 and 1000 have no common factors other than 1)
Part 3: Fraction to Decimal and Addition
  1. Convert each fraction to decimal:
  • \( \frac{5}{16} = 5 \div 16 = 0.3125 \)
  • \( \frac{3}{32} = 3 \div 32 = 0.09375 \)
  • \( \frac{5}{32} = 5 \div 32 = 0.15625 \)
  1. Add the decimals: \( 0.3125 + 0.09375 + 0.15625 = 0.5625 \)
  • Alternatively, add the fractions directly: \( \frac{5}{16} + \frac{3}{32} + \frac{5}{32} = \frac{10}{32} + \frac{3}{32} + \frac{5}{32} = \frac{18}{32} = \frac{9}{16} = 0.5625 \)
Part 4: Circumference Calculation (using \( C = \pi d \), \( \pi \approx 3.14 \))
  1. Diameter \( d = 5 \): \( C = 3.14 \times 5 = 15.7 \)
  2. Diameter \( d = 7 \): \( C = 3.14 \times 7 = 21.98 \)
  3. Diameter \( d = 2 \): \( C = 3.14 \times 2 = 6.28 \)
  4. Diameter \( d = 3\frac{3}{16} = \frac{51}{16} \): \( C = 3.14 \times \frac{51}{16} \approx 3.14 \times 3.1875 = 10.00875 \)
  5. Diameter \( d = 4\frac{1}{8} = \frac{33}{8} \): \( C = 3.14 \times \frac{33}{8} \approx 3.14 \times 4.125 = 12.9525 \)
  6. Diameter \( d = 4\frac{5}{16} = \frac{69}{16} \): \( C = 3.14 \times \frac{69}{16} \approx 3.14 \times 4.3125 = 13.54125 \)
  7. Diameter \( d = 7\frac{1}{32} = \frac{225}{32} \): \( C = 3.14 \times \frac{225}{32} \approx 3.14 \times 7.03125 = 22.078125 \)
  8. Diameter \( d = 8\frac{5}{8} = \frac{69}{8} \): \( C = 3.14 \times \frac{69}{8} \approx 3.14 \times 8.625 = 27.0825 \)
  9. Diameter \( d = \frac{3}{32} \): \( C = 3.14 \times \frac{3}{32} \approx 0.294375 \)
  10. Diameter \( d = 8\frac{1}{4} = \frac{33}{4} \): \( C = 3.14 \times \frac{33}{4} = 3.14 \times 8.25 = 25.905 \)
  11. Diameter \( d = 9\frac{5}{32} = \frac{293}{32} \): \( C = 3.14 \times \frac{293}{32} \approx 3.14 \times 9.15625 = 28.750625 \)
  12. Diameter \( d = 11\frac{3}{64} = \frac{707}{64} \): \( C = 3.14 \times \frac{707}{64} \approx 3.14 \times 11.046875 = 34.687125 \)

Answer:

Part 1: Fraction to Decimal Conversion
  1. \( \frac{1}{8} \): Divide 1 by 8. \( 1 \div 8 = 0.125 \)
  2. \( \frac{1}{4} \): Divide 1 by 4. \( 1 \div 4 = 0.25 \)
  3. \( \frac{3}{8} \): Divide 3 by 8. \( 3 \div 8 = 0.375 \)
  4. \( \frac{1}{2} \): Divide 1 by 2. \( 1 \div 2 = 0.5 \)
  5. \( \frac{5}{8} \): Divide 5 by 8. \( 5 \div 8 = 0.625 \)
  6. \( \frac{3}{4} \): Divide 3 by 4. \( 3 \div 4 = 0.75 \)
  7. \( \frac{7}{8} \): Divide 7 by 8. \( 7 \div 8 = 0.875 \)
Part 2: Decimal to Fraction Conversion
  1. \( 0.062 \): \( 0.062 = \frac{62}{1000} = \frac{31}{500} \)
  2. \( 0.125 \): \( 0.125 = \frac{125}{1000} = \frac{1}{8} \)
  3. \( 0.312 \): \( 0.312 = \frac{312}{1000} = \frac{39}{125} \)
  4. \( 0.187 \): \( 0.187 = \frac{187}{1000} \) (since 187 and 1000 have no common factors other than 1)
  5. \( 0.750 \): \( 0.750 = \frac{750}{1000} = \frac{3}{4} \)
  6. \( 0.875 \): \( 0.875 = \frac{875}{1000} = \frac{7}{8} \)
  7. \( 0.937 \): \( 0.937 = \frac{937}{1000} \) (since 937 and 1000 have no common factors other than 1)
Part 3: Fraction to Decimal and Addition
  1. Convert each fraction to decimal:
  • \( \frac{5}{16} = 5 \div 16 = 0.3125 \)
  • \( \frac{3}{32} = 3 \div 32 = 0.09375 \)
  • \( \frac{5}{32} = 5 \div 32 = 0.15625 \)
  1. Add the decimals: \( 0.3125 + 0.09375 + 0.15625 = 0.5625 \)
  • Alternatively, add the fractions directly: \( \frac{5}{16} + \frac{3}{32} + \frac{5}{32} = \frac{10}{32} + \frac{3}{32} + \frac{5}{32} = \frac{18}{32} = \frac{9}{16} = 0.5625 \)
Part 4: Circumference Calculation (using \( C = \pi d \), \( \pi \approx 3.14 \))
  1. Diameter \( d = 5 \): \( C = 3.14 \times 5 = 15.7 \)
  2. Diameter \( d = 7 \): \( C = 3.14 \times 7 = 21.98 \)
  3. Diameter \( d = 2 \): \( C = 3.14 \times 2 = 6.28 \)
  4. Diameter \( d = 3\frac{3}{16} = \frac{51}{16} \): \( C = 3.14 \times \frac{51}{16} \approx 3.14 \times 3.1875 = 10.00875 \)
  5. Diameter \( d = 4\frac{1}{8} = \frac{33}{8} \): \( C = 3.14 \times \frac{33}{8} \approx 3.14 \times 4.125 = 12.9525 \)
  6. Diameter \( d = 4\frac{5}{16} = \frac{69}{16} \): \( C = 3.14 \times \frac{69}{16} \approx 3.14 \times 4.3125 = 13.54125 \)
  7. Diameter \( d = 7\frac{1}{32} = \frac{225}{32} \): \( C = 3.14 \times \frac{225}{32} \approx 3.14 \times 7.03125 = 22.078125 \)
  8. Diameter \( d = 8\frac{5}{8} = \frac{69}{8} \): \( C = 3.14 \times \frac{69}{8} \approx 3.14 \times 8.625 = 27.0825 \)
  9. Diameter \( d = \frac{3}{32} \): \( C = 3.14 \times \frac{3}{32} \approx 0.294375 \)
  10. Diameter \( d = 8\frac{1}{4} = \frac{33}{4} \): \( C = 3.14 \times \frac{33}{4} = 3.14 \times 8.25 = 25.905 \)
  11. Diameter \( d = 9\frac{5}{32} = \frac{293}{32} \): \( C = 3.14 \times \frac{293}{32} \approx 3.14 \times 9.15625 = 28.750625 \)
  12. Diameter \( d = 11\frac{3}{64} = \frac{707}{64} \): \( C = 3.14 \times \frac{707}{64} \approx 3.14 \times 11.046875 = 34.687125 \)