MH Police Bharti · Bite-size lessons
Number System
About 6 min · Mathematics · English
Time worked out from the lesson's 356 words at 150 words a minute, plus a minute for each question.
The Number System forms the backbone of the entire Mathematics section in Maharashtra Police Bharti examination. Almost every arithmetic problem—whether percentage, ratio, or simplification—requires a solid understanding of different types of numbers and their properties.
Key ideas
- Natural Numbers (N): Counting numbers starting from 1. Set = {1, 2, 3, 4, ...}. Does NOT include zero.
- Whole Numbers (W): Natural numbers plus zero. Set = {0, 1, 2, 3, ...}. Every natural number is a whole number, but 0 is whole only.
- Integers (Z): Whole numbers plus negative numbers. Set = {..., -3, -2, -1, 0, 1, 2, 3, ...}. Includes positive, negative, and zero.
- Rational Numbers (Q): Numbers expressible as p/q where p and q are integers and q ≠ 0. Examples: 3/4, -7/2, 5 (which is 5/1), 0.25 (which is 1/4).
- Hierarchy: Natural ⊂ Whole ⊂ Integer ⊂ Rational. Every natural number is rational, but not vice versa.
Watch out for
- Thinking 0 is not a whole number → 0 IS a whole number but NOT a natural number. Remember: Whole = Natural + Zero.
- Calling 1 a prime number → 1 is NEITHER prime NOR composite. Prime numbers must have exactly two distinct factors; 1 has only one factor (itself).
- Confusing divisibility by 4 and 8 → For 4, check last TWO digits. For 8, check last THREE digits. Students often check only the last digit for both.
Quick reference
- N ⊂ W ⊂ Z ⊂ Q: Natural inside Whole inside Integer inside Rational
- 1 is neither prime nor composite; 2 is the only even prime
- Divisible by 6 = Divisible by BOTH 2 and 3
- Sum of first n naturals = n(n+1)/2
- For divisibility by 11: (Sum of odd-position digits) − (Sum of even-position digits) must be 0 or divisible by 11
Check yourself: 3 questions
1. What is the sum of the smallest natural number and the smallest whole number?
2. Which of the following is a rational number but not an integer?
3. If a number when divided by 5 leaves a remainder of 3, and when divided by 7 leaves a remainder of 4, what is the smallest such positive number?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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