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Decimal Fractions

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Quantitative Aptitude - Decimal Fractions

Learn definitions, operations, and tricks to solve quickly and score high.

1. What Is a Decimal Fraction?

A decimal fraction has a denominator that is a power of 10 (10, 100, 1000, ...). It can be represented in decimal form, e.g., 1/10 = 0.1, 7/100 = 0.07.

2. Conversion Between Fractions and Decimals

  • To convert a fraction with denominator \( 10^n \) into decimal: divide numerator by \( 10^n \). For example, \( \frac{56}{1000} = 0.056 \)
  • To convert decimal to fraction: count decimal places, place number over \( 10^n \), and simplify. For example, \( 0.0024 = \frac{24}{10000} = \frac{3}{1250} \)

3. Basic Operations

  • Add/Subtract: Align decimal points, then compute as whole numbers.
  • Multiply: Ignore decimals initially, multiply as integers, then place the decimal point equal to the total decimal places in both numbers. For example, \( 2.3 \times 0.12 = 0.276 \)
  • Divide by integer: Remove decimal, divide as whole numbers, then place the decimal in the quotient.
  • Divide by decimal: Multiply both numerator and denominator by 10ⁿ to convert divisor into a whole number, then divide.

4. Recurring Decimals

  • Pure recurring: All digits repeat (e.g., \( 0.\overline{3} \)). Convert using: numerator = repeating digits, denominator = equal number of 9s. \( 0.\overline{3} = \frac{3}{9} = \frac{1}{3} \)
  • Mixed recurring: Some digits repeat after a few fixed digits (e.g., \( 0.26\overline{6} \)). Use: \( \frac{266 - 26}{990} = \frac{240}{990} = \frac{4}{15} \)

5. Quick Exam Tips

  • Ignore decimals, compute, then insert the decimal at the end.
  • Count decimal digits carefully while multiplying and dividing.
  • Memorize recurring decimal to fraction conversions.
  • Compare decimals by padding zeros as needed (e.g., 0.7 and 0.70 are equal).
  • Know fraction to decimal conversions for common values: \( \frac{1}{2} = 0.5 \), \( \frac{1}{4} = 0.25 \), etc.

6. Revision Checklist

  • Master fraction ↔ decimal conversion in both directions.
  • Comfortably handle addition, subtraction, multiplication, and division of decimals.
  • Convert recurring and mixed recurring decimals quickly.
  • Practice simplifying decimals in word problems under time pressure.

Summary: Understand decimal basics, apply operations with care, and remember recurring rules. Avoid manual errors in placement of decimal points and you'll master this topic easily.

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