Decimal and Fractions for SSC CGL - Complete Guide | Conversion & Comparison Tricks in Hindi

By FinishSTUDY Editorial Team • • •
📌 Series Info: Ye post Chapter 1: Number System ka part hai.
Post Number: 10/76 | Topic: 1.10 Decimal & Fractions
Previous: 1.1-1.9 Complete ✅

Introduction: Decimal Aur Fractions Kya Hain?

Namaste dosto! Aaj ham Decimals (दशमलव) aur Fractions (भिन्न) padhenge. Ye number system ka essential part hai aur SSC CGL me bahut questions aate hain.

Fraction Kya Hai?

🔹 Fraction = Numerator / Denominator
Form: p/q (jahan q ≠ 0)
Examples:
1/2 (Numerator = 1, Denominator = 2)
3/4 (Numerator = 3, Denominator = 4)
7/8, 5/6, 11/13, etc.

Decimal Kya Hai?

🔹 Decimal = Numbers jo decimal point (.) ke saath likhe jaate hain
Parts: Integer part + Decimal part
Examples:
0.5 (Integer = 0, Decimal = 5)
3.75 (Integer = 3, Decimal = 75)
12.345, 0.125, 99.99, etc.
🎯 Exam Importance: SSC CGL me questions aate hain:
  • Fraction to decimal conversion
  • Decimal to fraction conversion
  • Recurring decimals identification
  • Comparison of fractions/decimals
  • Operations (addition, subtraction, multiplication, division)
  • Simplification problems

Types of Fractions

1. Proper Fraction (उचित भिन्न)

Numerator < Denominator
Value hamesha 1 se chhota
Examples: 1/2, 3/4, 5/8, 7/10
Sab values 1 se chhoti hain (0.5, 0.75, 0.625, 0.7)

2. Improper Fraction (अनुचित भिन्न)

Numerator ≥ Denominator
Value hamesha 1 se badi ya equal
Examples: 5/4, 7/3, 11/5, 8/8
Values: 1.25, 2.33, 2.2, 1

3. Mixed Fraction (मिश्र भिन्न)

Integer part + Proper fraction
Form: a b/c
Examples: 2 1/2, 3 3/4, 5 2/3
Conversion to improper:
2 1/2 = (2×2 + 1)/2 = 5/2 ✓

4. Like Fractions (समान भिन्न)

Same denominator wale fractions
Examples: 1/5, 3/5, 7/5 (sab ka denominator 5)

5. Unlike Fractions (असमान भिन्न)

Different denominators
Examples: 1/2, 2/3, 3/4 (sab ka denominator alag)

Types of Decimals

1. Terminating Decimal (समाप्त होने वाला)

Decimal jo khatam ho jaaye (limited digits)
Examples:
0.5, 0.25, 0.125, 3.75, 12.8
Ye sab finite decimal places ke baad khatam ho jate hain

2. Non-Terminating Decimal (अनन्त दशमलव)

Decimal jo kabhi khatam na ho (infinite digits)

3. Recurring/Repeating Decimal (आवर्ती दशमलव)

Non-terminating decimal jisme digit pattern repeat hota hai
Notation: Bar (—) repeating digits ke upar
Examples:
0.333... = 0.3̄ (3 repeat)
0.666... = 0.6̄ (6 repeat)
0.142857142857... = 0.1̄4̄2̄8̄5̄7̄ (142857 repeat)
0.1666... = 0.16̄ (sirf 6 repeat)

4. Non-Recurring Decimal (अनावर्ती दशमलव)

Non-terminating aur non-repeating
Ye irrational numbers hote hain
Examples:
Ï€ = 3.14159265...
√2 = 1.41421356...
e = 2.71828182...

Fraction to Decimal Conversion IMPORTANT

Fraction ko decimal me convert karne ke liye:
Numerator ÷ Denominator

Terminating Decimals

Example 1: 1/2 = ?
1 ÷ 2 = 0.5 ✓
Example 2: 3/4 = ?
3 ÷ 4 = 0.75 ✓
Example 3: 7/8 = ?
7 ÷ 8 = 0.875 ✓

Recurring Decimals

Example 1: 1/3 = ?
1 ÷ 3 = 0.333... = 0.3̄ ✓
Example 2: 2/3 = ?
2 ÷ 3 = 0.666... = 0.6̄ ✓
Example 3: 1/7 = ?
1 ÷ 7 = 0.142857142857... = 0.1̄4̄2̄8̄5̄7̄ ✓

Common Fractions & Their Decimal Values (Yaad Karo!)

Fraction Decimal Fraction Decimal
1/20.5 1/110.0̄9̄
1/30.3̄ 2/110.1̄8̄
2/30.6̄ 3/110.2̄7̄
1/40.25 1/120.083̄
3/40.75 1/130.0̄7̄6̄9̄2̄3̄
1/50.2 1/150.06̄
2/50.4 1/160.0625
3/50.6 1/200.05
4/50.8 1/250.04
1/60.16̄ 1/500.02
5/60.83̄ 1/1000.01
1/70.1̄4̄2̄8̄5̄7̄ 1/80.125
1/90.1̄ 3/80.375
2/90.2̄ 5/80.625
1/100.1 7/80.875
💡 Memory Tip: Kam se kam 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9 yaad karo. Exam me instant use kar sakte ho!

Decimal to Fraction Conversion

Method 1: Terminating Decimals

Example 1: 0.5 = ?
Step 1: Denominator = 10 (1 decimal place)
0.5 = 5/10
Step 2: Simplify
5/10 = 1/2 ✓
Example 2: 0.75 = ?
Denominator = 100 (2 decimal places)
0.75 = 75/100 = 3/4 ✓
Example 3: 0.125 = ?
Denominator = 1000 (3 decimal places)
0.125 = 125/1000 = 1/8 ✓

Method 2: Recurring Decimals

⭐ Pure Recurring: 0.x̄ = x/9
⭐ 0.x̄ȳ = xy/99
⭐ Mixed Recurring: 0.ax̄ = (ax - a)/90
Example 1: 0.3̄ = ?
Pure recurring (sirf 3 repeat)
0.3̄ = 3/9 = 1/3 ✓
Example 2: 0.6̄ = ?
0.6̄ = 6/9 = 2/3 ✓
Example 3: 0.2̄7̄ = ?
Two digits repeat
0.2̄7̄ = 27/99 = 3/11 ✓
Example 4: 0.16̄ = ? (Mixed recurring)
Non-recurring part = 1, Recurring part = 6
0.16̄ = (16 - 1)/90 = 15/90 = 1/6 ✓
Example 5: 0.83̄ = ?
0.83̄ = (83 - 8)/90 = 75/90 = 5/6 ✓

Fractions/Decimals Ko Compare Kaise Karein?

Method 1: Convert to Decimal

Example: Kaun bada hai: 2/3 ya 3/4?
2/3 = 0.666...
3/4 = 0.75
0.75 > 0.666
Answer: 3/4 > 2/3 ✓

Method 2: Cross Multiplication

a/b aur c/d compare karne ke liye:
a × d vs b × c
Example: 5/7 vs 7/9?
Cross multiply:
5 × 9 = 45
7 × 7 = 49
49 > 45
Answer: 7/9 > 5/7 ✓

Method 3: Make Denominators Equal

Example: 3/5 vs 4/7?
LCM(5,7) = 35
3/5 = 21/35
4/7 = 20/35
21 > 20
Answer: 3/5 > 4/7 ✓

Operations With Fractions

Addition/Subtraction

Same denominator: a/c + b/c = (a+b)/c
Different denominators: LCM nikalo
Example: 1/4 + 1/6 = ?
LCM(4,6) = 12
1/4 = 3/12
1/6 = 2/12
Sum = (3+2)/12 = 5/12 ✓

Multiplication

a/b × c/d = (a×c)/(b×d)
Example: 2/3 × 3/4 = ?
(2×3)/(3×4) = 6/12 = 1/2 ✓

Division

a/b ÷ c/d = a/b × d/c (reciprocal se multiply)
Example: 3/4 ÷ 2/3 = ?
3/4 × 3/2 = 9/8 ✓

SSC CGL Level Practice Questions

Q1. 0.5̄4̄ ko fraction me convert karo
(A) 5/9
(B) 54/99
(C) 6/11
(D) 49/90

Answer: (C) 6/11
Solution:
Two digits repeat: 54
0.5̄4̄ = 54/99 = 6/11 ✓
Q2. 3/7 aur 5/9 me kaun bada hai?
(A) 3/7
(B) 5/9
(C) Equal
(D) Cannot determine

Answer: (B) 5/9
Solution:
Cross multiply: 3×9 = 27, 7×5 = 35
35 > 27, so 5/9 > 3/7 ✓
Q3. (2/3 + 3/4) × 6 = ?
(A) 8.5
(B) 8
(C) 9
(D) 10

Answer: (A) 8.5
Solution:
2/3 + 3/4 = 8/12 + 9/12 = 17/12
17/12 × 6 = 17/2 = 8.5 ✓
Q4. 0.125 ka fraction form kya hoga?
(A) 1/6
(B) 1/7
(C) 1/8
(D) 1/9

Answer: (C) 1/8
Solution:
0.125 = 125/1000 = 1/8 ✓
Q5. Niche diye fractions ko ascending order me arrange karo: 2/3, 3/5, 5/8
(A) 2/3, 5/8, 3/5
(B) 3/5, 5/8, 2/3
(C) 5/8, 3/5, 2/3
(D) 3/5, 2/3, 5/8

Answer: (B) 3/5, 5/8, 2/3
Solution:
Decimal form: 2/3 = 0.666, 3/5 = 0.6, 5/8 = 0.625
Ascending: 0.6 < 0.625 < 0.666
So: 3/5 < 5/8 < 2/3 ✓

Exam Shortcuts & Tricks

🚀 Trick 1: 1/7 Pattern
1/7 = 0.142857 (ye 6 digits repeat karte hain)
2/7 = 0.285714 (same digits, different starting point)
3/7 = 0.428571, 4/7 = 0.571428, etc.
🚀 Trick 2: 1/9 Pattern
1/9 = 0.1̄, 2/9 = 0.2̄, 3/9 = 0.3̄...
Pattern simple hai: numerator hi repeat hota hai!
🚀 Trick 3: Powers of 2 in Denominator
2, 4, 8, 16, 32... ka denominator hamesha terminating decimal deta hai
1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 1/16 = 0.0625
🚀 Trick 4: Quick Comparison
Agar numerators equal hain: Chhota denominator = Bada fraction
1/3 > 1/4 > 1/5 ✓

Homework Practice (Khud Try Karo)

  1. 0.36̄ ko fraction me convert karo
  2. 5/12 aur 7/15 me kaun bada hai?
  3. 1/7 ka decimal expansion 50 digits tak likho (pattern dekho)
  4. (3/5 - 1/3) × 15 = ?
  5. 0.2̄7̄3̄ ko fraction me convert karo

Common Mistakes (Ye Galtiyan Mat Karna)

❌ Mistake 1: Recurring decimal me galat formula use karna
0.3̄ ≠ 3/10 ✗
0.3̄ = 3/9 = 1/3 ✓
❌ Mistake 2: Fractions add/subtract karte waqt denominators add karna
1/2 + 1/3 ≠ 2/5 ✗
1/2 + 1/3 = 5/6 ✓
❌ Mistake 3: Division me reciprocal lena bhool jaana
a/b ÷ c/d = a/b × d/c (reciprocal!) ✓

Next Topic Preview

📚 Agle Post Me: 1.11 Simplification & BODMAS
BODMAS rules, simplification techniques, complex expressions solve karna, shortcuts aur SSC level questions!

Conclusion

Decimal aur Fractions number system ki neev hain. Conversion methods aur common fractions yaad karo – exam me bahut time bachega!

Daily Practice: Random fractions ka decimal form aur vice versa practice karo. Speed aur accuracy dono improve honge!

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