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History of Numbers and Digits

● Use of Fingers in Ancient Times & Origin of the Word ‘Digit’

• Early humans had no written number system.
• They counted objects using fingers.
• The tips of the fingers were called digits.
• Therefore, the word “Digit” originally meant a counting point/finger unit.
• With time, the same became the modern digits (0–9).

● Development of Number Systems

• Initially numbers were recorded by marks, stones, and lines.
• Egyptians (3000 BCE) used pictorial symbols.
• Babylonians developed a base-60 system.
• Romans used symbols like I, V, X, L, C, D, M.
• India developed the most advanced system including the invention of Zero (0).
• Indian mathematicians like Aryabhata and Brahmagupta formalized the place-value decimal system.
• Through Arab scholars, the Indian system spread globally and became known as the Hindu-Arabic Number System.

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Meaning (Etymology) of Number and Digit

● Digit

• Originally meant finger tip used for counting.
• Today, digits are 0 to 9.

● Number

• A number is a combination of digits representing a value.
• Example: 7 (digit), 735 (number).
• The word “Number” comes from the Sanskrit root “Sankh” meaning to count.

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Number System (Types)

Meaning

A number system is a method of representing numbers using specific digits and rules.

Major Number Systems

• Decimal (Base 10)
• Binary (Base 2)
• Octal (Base 8)
• Hexadecimal (Base 16)

Base / Radix

Base = Total number of digits used in a system.
Examples:

• Decimal → Base 10 → Digits (0–9)
• Binary → Base 2 → Digits (0,1)
• Octal → Base 8 → Digits (0–7)
• Hexadecimal → Base 16 → Digits (0–9, A–F)

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Decimal Number System

Introduction

• Most widely used number system.
• Developed from the Indian mathematical tradition.

Base

• Base = 10
• Digits used = 0 to 9

Types of Numbers (Basic Exam Concepts)

1. Natural Numbers

• Counting numbers: 1, 2, 3, …

2. Whole Numbers

• Natural numbers including 0:
  0, 1, 2, 3, …

3. Integers

• Negative, positive and zero:
  …, –3, –2, –1, 0, 1, 2 …

4. Rational Numbers

• Numbers written in the form a/b, where b ≠ 0.

5. Irrational Numbers

• Cannot be expressed as a/b:
  √2, π, etc.

6. Real Numbers

• Rational + Irrational.

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Place Value & Face Value (with Examples)

Face Value

• The value of a digit itself.
• Example: In 582, Face Value of 8 = 8

Place Value

• Value of a digit according to its position.
• Example: In 582, Place Value of 8 = 8 × 10 = 80

Example (Full Explanation)

Number = 4 7 2 5

• Place Value of 5 = 5 × 1 = 5
• Place Value of 2 = 2 × 10 = 20
• Place Value of 7 = 7 × 100 = 700
• Place Value of 4 = 4 × 1000 = 4000

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Basic Number-Based Questions (Solved)

Largest & Smallest Numbers

• Largest 2-digit number → 99
• Smallest 2-digit number → 10
• Largest 1-digit number → 9
• Smallest 1-digit number → 0
• Smallest 3-digit number → 100
• Largest 3-digit number → 999
• Smallest 4-digit number → 1000
• Largest 4-digit number → 9999

Place Value Questions

Q: Place value of 6 in 7685?
→ 6 × 100 = 600

Face Value Question

Q: Face value of 6 in 7685?
→ 6

Type of Numbers Question

Q: Is 0 a natural number?
→ No, it is a whole number.

Q: Is –5 an integer?
→ Yes.

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20 MCQs (with Answers)

1. The word ‘Digit’ originates from—
A) Stone B) Finger C) Line D) Picture
Ans: B

2. Base of Decimal system is—
A) 2 B) 8 C) 10 D) 16
Ans: C

3. Digits used in Binary system—
A) 0–9 B) 0–7 C) 0–1 D) 0–5
Ans: C

4. Base of Octal system is—
A) 10 B) 8 C) 16 D) 2
Ans: B

5. Face value of 7 is—
A) Depends on place B) 7 C) 70 D) 700
Ans: B

6. Place value of 7 in 5728—
A) 7 B) 70 C) 700 D) 7000
Ans: C

7. Smallest 3-digit number—
A) 099 B) 100 C) 101 D) 111
Ans: B

8. Largest 2-digit number—
A) 90 B) 99 C) 100 D) 89
Ans: B

9. Value of A in Hexadecimal—
A) 8 B) 9 C) 10 D) 11
Ans: C

10. Which is a rational number?
A) √2 B) π C) 5/7 D) All
Ans: C

11. Which is NOT an integer?
A) 5 B) –2 C) 0 D) 5.3
Ans: D

12. Place value of 3 in 4321—
A) 3 B) 30 C) 300 D) 3000
Ans: C

13. 0 belongs to which category?
A) Natural B) Whole C) Irrational D) Not real
Ans: B

14. Which is a decimal digit?
A) A B) G C) 9 D) H
Ans: C

15. –7 is which type of number?
A) Integer B) Natural C) Whole D) Non-rational
Ans: A

16. Highest place value in 9999 belongs to—
A) Units B) Tens C) Hundreds D) Thousands
Ans: D

17. Place-value system originated in—
A) Greece B) India C) China D) Egypt
Ans: B

18. Place value of 0 in 2045—
A) 0 B) 100 C) 1000 D) 10
Ans: B

19. Which system has the highest base?
A) Binary B) Octal C) Decimal D) Hexadecimal
Ans: D

20. Which is a natural number?
A) 0 B) –1 C) 1 D) –5
Ans: C

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