Decimal and Fraction
Decimals and fractions are fundamental concepts in quantitative aptitude used in percentage, ratio, profit & loss, and many other topics. Fast conversion between them is essential for solving questions quickly.
Fundamental Principles
Fraction
A number expressed as p/q, where q ≠ 0.
Decimal
A number expressed in base 10 with a decimal point.
Recurring Decimal
A decimal that repeats its digits infinitely.
Essential Formulation Tips
- Memorize common fraction-decimal values (1/2 = 0.5, 1/4 = 0.25).
- Convert fractions to decimals for quick comparison.
- Use multiplication for recurring decimal conversion.
- Practice fast mental calculations.
Shortcut Execution Techniques
- 1/3 = 0.333..., 2/3 = 0.666...
- 1/8 = 0.125, 1/16 = 0.0625.
- Recurring decimal to fraction: x = 0.333 → 10x − x = 3 → x = 1/3.
- Multiply numerator & denominator to simplify.
Contextual Inquiries (FAQs)
Q: What is the fastest way to convert fraction to decimal?
A:
Q: How to convert recurring decimal to fraction?
A:
Example Breakdown: Fraction to Decimal
Basic conversion.1 ÷ 4 = 0.25.
Final Answer: 0.25.
Example Breakdown: Decimal to Fraction
Important concept.0.75 = 75/100.
Simplify → 3/4.
Final Answer: 3/4.
Example Breakdown: Recurring Decimal
High scoring question.Let x = 0.333...
10x = 3.333...
10x − x = 3.
9x = 3 → x = 1/3.
Final Answer: 1/3.
Decimal & Fraction Practice Questions
Solve important decimal and fraction questions for banking, SSC, CMAT, and placement exams.
Q1. Convert 1/5 into decimal.
Q2. Convert 0.125 into fraction.
Q3. Convert 0.666... into fraction.