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.