Class Notes: Converting Fractions to Decimals Mentally

Objective

Learn how to convert fractions to decimals quickly without using long division or a calculator, mainly through memorization of common fraction-decimal equivalents.

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Key Fraction-to-Decimal Conversions to Memorize

| Fraction | Decimal Equivalent | |-----------|------------------------| | 1/2 | 0.5 | | 1/3 | 0.333... (repeating) | | 1/4 | 0.25 | | 1/5 | 0.2 | | 1/6 | 0.166... (repeating) | | 1/7 | ~0.143 (rounded) | | 1/8 | 0.125 | | 1/9 | 0.111... (repeating) | | 1/10 | 0.1 | | 1/16 | 0.0625 | | 1/20 | 0.05 | | 1/25 | 0.04 | | 1/50 | 0.02 | | 1/100 | 0.01 | | 1/1000 | 0.001 |

“Nines” Patterns

• 2/9 = 0.222...
• 4/9 = 0.444...
• 23/99 = 0.2323... (repeating)
• 17/99 = 0.1717... (repeating)
• 247/999 = 0.247247... (repeating)

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Strategies

Proper Fractions

• Use the memorized values for the most common fractions.
• Multiply the numerator by the decimal value of the denominator’s reciprocal (if easily memorized).

Examples

1. 2/3:
   1/3 = 0.333... ⇒ 2 × 0.333... = 0.666...
2. 3/4:
   1/4 = 0.25 ⇒ 3 × 0.25 = 0.75
3. 4/5:
   1/5 = 0.2 ⇒ 4 × 0.2 = 0.8

Reducing Fractions

• Always check if fractions can be simplified before converting.

  • 5/20 → reduces to 1/4 = 0.25
  • 3/10 = 3 × 0.1 = 0.3
  • 7/100 = 7 × 0.01 = 0.07

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Improper Fractions

• Break into “whole” and “remainder” parts for easier calculation.

  1. 9/4:
     8/4 + 1/4 = 2 + 0.25 = 2.25
  2. 8/5:
     5/5 + 3/5 = 1 + (3 × 0.2) = 1.6
  3. 35/8:
     32/8 + 3/8 = 4 + (3 × 0.125 = 0.375) = 4.375

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Additional Practice

• 4/25: 4 × 0.04 = 0.16
• 17/1000: 17 × 0.001 = 0.017

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Patterns and Takeaways

• Fractions with denominators of 10, 100, 1000, 20, 25, 50, etc., convert easily by multiplying the numerator with the fraction’s decimal equivalent.
• For nines, the numerator as repeating digits (e.g., 23/99 = 0.2323...).
• Reduce the fraction first if possible for easier computation.

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Conclusion

Memorizing the decimal values of common fractions (about 10–15 key values) allows you to quickly and accurately convert most fractions to decimals mentally and efficiently, without tools. Practice regularly to reinforce recall and speed.

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Tip: Keep a reference sheet of these key fraction-decimal equivalents for review until you have them memorized!