Introduction to Number Systems

Hello Students! 👋

Aaj hum Maths ke ek bahut important aur basic chapter — Number System ke baare me poori detail me padhenge.

Numbers humein har jagah milte hain:

Isliye, numbers ko samajhna Maths ka foundation hota hai.

Iss chapter me hum different types of numbers ko seekhenge aur samjhenge ki kaise hum unhe identify, compare, visualize aur use karte hain.

🎥 Video Explanation

🇮🇳 Hindi Explanation

🇬🇧 English Explanation

📊 Infographic Summary

Infographic Summary

🧭 Number Line Kya Hoti Hai?

📖 Story Time: The Infinite Road

Imagine karo ek lambi, seedhi road jo kabhi khatam nahi hoti. Aap ek milestone par khade ho jahan 0 likha hai. Agar aap aage (Right) badhte ho, toh aap milestones 1, 2, 3... cross karte ho. Agar aap peeche (Left) jaate ho, toh aap milestones -1, -2, -3... cross karte ho. Ye road humein dikhati hai ki har number kahan rehta hai!

Number Line ek seedhi horizontal line hoti hai jisme numbers ko equal distance par mark kiya jaata hai. Iska use hum numbers ko visualize karne, compare karne, ya addition–subtraction jaise operations samajhne ke liye karte hain.

✔ Basic Structure of Number Line

← ... -4, -3, -2, -1 | 0 | 1, 2, 3, 4, ... →

📌 Important Points:

  • 0 center me hota hai.
  • Right side me positive numbers hote hain (→ 1, 2, 3, 4…).
  • Left side me negative numbers hote hain (→ -1, -2, -3, -4…).
  • Jitna right jaoge → number bada hota jaata hai.
  • Jitna left jaoge → number chhota hota jaata hai.

✔ Example:

Number line par kaun bada hai?

  • 3 ya -5?
    → 3 right side me hai, toh 3 > -5.
  • -2 ya 0?
    → 0 hamesha negative numbers se bada hota hai.

🔢 Types of Numbers (Detailed Explanation)

Ab hum numbers ko unke types ke hisaab se samjhenge. Har type me example + diagram hoga.

1️⃣ Natural Numbers (N)

📖 Story Time: The Shepherd's Counting

Imagine karo purane zamane me jab ek shepherd (gadariya) apni bhedon (sheep) ko ginna chahta tha. Woh ginti shuru karta tha: "Ek sheep, do sheep, teen sheep..." aur aise hi aage. Ye counting numbers uske dimaag me naturally aaye, isliye hum inhe Natural Numbers kehte hain.

Natural numbers woh numbers hote hain jo hum ginti karne ke liye use karte hain. Ye hamesha 1 se shuru hote hain aur infinite tak jaate hain.

✔ Definition: Numbers used for counting objects.

✔ Symbol: N

✔ Set Representation: N = {1, 2, 3, 4, 5, …}

✔ Real-life Examples:

  • 5 students
  • 12 pens
  • 8 mangoes

📌 Important Notes:

  • 0 natural number nahi hota.
  • Natural numbers kabhi khatam nahi hote (infinite hote hain).

2️⃣ Whole Numbers (W)

📖 Story Time: The Empty Basket

Ek din, us shepherd ne apni saari sheep bech di. Usne apne khaali pen (baade) ko dekha aur socha, "Main kuch nahi (nothing) ko kaise likhun?" Natural numbers (1, 2, 3...) kaafi nahi the. Toh, number Zero (0) introduce hua. Jab hum natural numbers me 0 ko add karte hain, toh woh set Whole ban jaata hai.

Whole numbers natural numbers ki extended form hain. Difference sirf itna hai ki Whole numbers me 0 bhi include hota hai.

✔ Definition: Natural numbers + 0

✔ Symbol: W

✔ Set Representation: W = {0, 1, 2, 3, 4, …}

✔ Difference Between Natural & Whole:

Feature Natural (N) Whole (W)
Starting number 1 0
0 include? ❌ No ✔ Yes
Infinite? ✔ ✔

✔ Real-life Examples:

  • 0 victory
  • 0 marks
  • 0 balance in wallet

💡 Important Point:
👉 Saare natural numbers whole numbers hote hain, but saare whole numbers natural numbers nahi hote (kyunki 0 natural number nahi hai).

3️⃣ Integers (Z)

📖 Story Time: The Shopkeeper's Ledger

Baad me, logon ne vyapaar (trading) shuru kiya. Ek shopkeeper paise kamata tha (profit) lekin kabhi-kabhi paise kho bhi deta tha (loss) ya udhaar leta tha (debt). ₹5 ka udhaar likhne ke liye, woh sirf "5" use nahi kar sakta tha. Use ek sign chahiye tha jo dikhaye ki ye paisa dena hai. Toh, Negative Numbers (-1, -2, -3...) ka janm hua. Whole numbers ke saath milkar, ye Integers banate hain.

Integers me positive numbers, negative numbers, aur zero sab include hote hain.

✔ Definition: Whole numbers + Negative numbers

✔ Symbol: Z (from the German word “Zahlen” which means “to count”)

✔ Set Representation: Z = {…, −3, −2, −1, 0, 1, 2, 3, …}

✔ Real-life Examples:

  • −5°C temperature
  • −3 goal difference
  • +7 marks increased

📌 Important Points:

  • Saare whole numbers integers hain.
  • Negative numbers bhi integers hote hain.
  • Integers dono direction me infinite hote hain.

4️⃣ Rational Numbers (Q)

📖 Story Time: The Pizza Party

Imagine karo tumhare paas 1 pizza hai aur tumhe use 2 doston me barabar baantna hai. Tum har kisi ko 1 poora pizza nahi de sakte. Tumhe use kaatna padega! Har kisi ko aadha (1/2) milega. Ye numbers, jo kisi cheez ka hissa (part) ya ratio dikhate hain, unhe Rational Numbers kehte hain.

Rational numbers wo hote hain jise hum p/q form me likh sakte hain.

✔ Definition:

A number of the form p/q, where:

✔ Symbol: Q (from Quotient)

✔ Set Examples:

  • 1/2
  • 3/4
  • -5/2
  • 0 (kyunki 0 = 0/1)
  • 7 (kyunki 7 = 7/1)

💡 Important Note:
👉 Kisi bhi do rational numbers ke beech me infinite rational numbers hote hain.

Example:

1/2 aur 1 ke beech me kitne rational numbers hain?
→ Infinite.

Because:

  • 1/2 = 0.5
  • 1 = 1.0

Between 0.5 and 1.0, you can write: 0.6, 0.7, 0.75, 0.8, 0.9… aur bohot saare.

📌 Aage Ka Content (Coming Next)

This page covers the basics. We will continue with the following topics in the next lessons: