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Number System

About 5 min · Mathematics · English

Time worked out from the lesson's 263 words at 150 words a minute, plus a minute for each question.

The Number System forms the foundation of quantitative aptitude in MPESB exams. Questions from this topic appear directly (identifying number types, finding LCM/HCF) and indirectly (as building blocks for percentages, ratios, and simplification problems).

Key ideas

• Natural Numbers (N): Counting numbers starting from 1. Set: {1, 2, 3, 4, ...}. Zero is NOT included.
• Whole Numbers (W): Natural numbers plus zero. Set: {0, 1, 2, 3, ...}. Every natural number is a whole number.
• Integers (Z): Whole numbers plus negatives. Set: {..., -3, -2, -1, 0, 1, 2, 3, ...}. Includes positive, negative, and zero.
• Rational Numbers (Q): Any number expressible as p/q where p and q are integers and q ≠ 0. Includes terminating decimals (0.25 = 1/4) and repeating decimals (0.333... = 1/3).
• Irrational Numbers: Cannot be expressed as p/q. Non-terminating, non-repeating decimals. Examples: √2, √3, π, e. Note: √4 = 2 is rational, not irrational.

Quick reference

• Whole numbers = {0, 1, 2, 3, ...}; Natural numbers start from 1.
• Rational = p/q form (includes terminating and repeating decimals); Irrational = non-repeating, non-terminating.
• HCF × LCM = Product of the two numbers (two numbers only).
• For LCM: take highest powers; For HCF: take lowest powers.
• Divisibility by 6 = check both 2 AND 3.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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