Number System — Study Notes for SSC MTS

Overview

The Number System is the foundation of all quantitative topics in SSC MTS Paper 1. Questions appear directly (classify number types, apply divisibility rules, work with fractions) and indirectly (every calculation question uses these concepts). Expect 3–5 direct questions from this topic and many more that require quick mental math based on number properties.

Mastery here means speed: identifying odd/even patterns instantly, applying divisibility tests without writing steps, and converting fractions-decimals fluently. The exam tests both conceptual understanding (is √2 rational?) and computational skill (simplify 3/7 + 2/5 in 15 seconds). Students who internalize divisibility rules and fraction shortcuts gain 2–3 minutes per paper — a decisive advantage in a time-bound exam.

Focus on integers, fractions (proper, improper, mixed), decimals, rational/irrational classification, and the big six divisibility rules (2, 3, 5, 9, 10, 11). Skip advanced number theory; SSC MTS stays with practical, calculation-heavy problems.

Key Concepts

• **Natural numbers** (1, 2, 3, ...) count discrete objects. **Whole numbers** add zero (0, 1, 2, ...). **Integers** include negatives (..., -2, -1, 0, 1, 2, ...). Every natural number is whole and every whole number is an integer.

• **Rational numbers** can be written as p/q where p and q are integers and q ≠ 0. All terminating and repeating decimals are rational (e.g. 0.75 = 3/4, 0.333... = 1/3). **Irrational numbers** cannot be expressed as fractions (e.g. √2, π, √3).

• **Even numbers** are divisible by 2 (last digit 0, 2, 4, 6, 8). **Odd numbers** are not (last digit 1, 3, 5, 7, 9). Sum of two evens is even; sum of two odds is even; sum of even and odd is odd.

• **Prime numbers** have exactly two factors: 1 and the number itself (2, 3, 5, 7, 11, 13, ...). Note: 1 is neither prime nor composite. 2 is the only even prime.

• **Composite numbers** have more than two factors (4, 6, 8, 9, 10, ...). Every composite number can be expressed as a product of primes (prime factorization).

• **Fractions**: Proper fraction (numerator < denominator, e.g. 3/4), improper fraction (numerator ≥ denominator, e.g. 7/4), mixed number (whole + proper fraction, e.g. 1¾). Convert improper to mixed: divide numerator by denominator; quotient is whole part, remainder over denominator is fractional part.

• **Divisibility rules** let you test if one number divides another without performing division. Essential for simplification, factorization, and LCM/HCF problems.

• **Place value** vs **face value**: In 3,425, the digit 4 has face value 4 but place value 400 (hundreds place). Sum of digits = 3+4+2+5 = 14.