Decimals and Fractions — RRB NTPC Study Notes

Overview

Decimals and fractions form the backbone of arithmetic computation in RRB NTPC exams. Expect 3–5 direct questions from this topic, plus its application in percentage, ratio, time-and-work, and data interpretation problems. Mastery here means speed and accuracy — a strong candidate converts between forms instinctively and performs operations without hesitation.

The syllabus demands fluency in interconversion (fraction ↔ decimal), all four arithmetic operations on both forms, simplification of complex expressions, and comparison of fractional/decimal quantities. Most errors stem from misplaced decimal points, incorrect denominator handling, and careless simplification. Treat this topic as foundational: once solid, it accelerates every other quantitative section.

Questions range from straightforward computation ("What is 0.125 + 3/8?") to multi-step word problems involving money, measurements, or mixture. The key is recognising when to keep numbers as fractions (for exact answers) versus decimals (for quick approximation).

Key Concepts

• **Fraction representation**: A fraction a/b represents division of a by b. The numerator (a) is the part; denominator (b) is the whole. Proper fraction: a < b. Improper fraction: a ≥ b. Mixed number: whole number + proper fraction (e.g., 2 3/4).

• **Decimal representation**: A decimal is another way to write fractions with denominators 10, 100, 1000, etc. The decimal point separates the whole part (left) from the fractional part (right). Each place to the right is one-tenth of the previous: tenths (0.1), hundredths (0.01), thousandths (0.001).

• **Conversion fraction → decimal**: Divide numerator by denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Terminating decimals end (like 0.5, 0.125); non-terminating decimals repeat forever (like 1/3 = 0.333...).

• **Conversion decimal → fraction**: Write the decimal as a fraction with denominator 10, 100, 1000 (depending on decimal places), then simplify. Example: 0.6 = 6/10 = 3/5. For repeating decimals, use the algebraic method (less common in RRB but good to know).

• **Like and unlike fractions**: Fractions with the same denominator are like fractions (can add/subtract directly). Unlike fractions need a common denominator first (usually the LCM of denominators).

• **Simplification**: Always reduce fractions to lowest terms by dividing numerator and denominator by their HCF. For decimals, remove trailing zeros after the decimal point (e.g., 2.500 = 2.5).

• **Order of operations**: BODMAS applies to both fractions and decimals. Simplify brackets first, then division/multiplication (left to right), then addition/subtraction (left to right).