Lesson 1.2: Decimals, Fractions, Percentages

SSC Exam Preparation: Complete Quant, Reasoning, English & GA Course

Introduction:
Decimals, fractions, and percentages are different ways to represent numbers. Understanding the relationship between them is crucial for solving questions in SSC exams.

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1. Decimals
– Definition: A decimal number is a number with a decimal point, which separates the whole number part and the fractional part.
Example: 12.45 (12 is the whole number, .45 is the fractional part)
– Place Values:
0.1 = Tenths
0.01 = Hundredths
0.001 = Thousandths
– Conversion to Fraction:
Example: 0.25 = 25/100 = 1/4

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2. Fractions
– Definition: A fraction represents a part of a whole in the form of p/q, where p = numerator, q = denominator.
Example: 3/4 means 3 parts out of 4.
– Types of Fractions:
• Proper Fraction: Numerator < Denominator (e.g., 3/5)
• Improper Fraction: Numerator ≥ Denominator (e.g., 7/4)
• Mixed Fraction: Combination of whole number and fraction (e.g., 2 1/2)
– Conversion to Decimal:
Divide numerator by denominator.
Example: 3/4 = 0.75

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3. Percentages
– Definition: A percentage is a fraction with denominator 100.
Example: 45% = 45/100 = 0.45
– Conversions:
• Fraction → Percentage: (Fraction × 100)%
Example: 3/8 × 100 = 37.5%
• Decimal → Percentage: (Decimal × 100)%
Example: 0.65 × 100 = 65%
• Percentage → Fraction: (Percentage ÷ 100)
Example: 80% = 80/100 = 4/5

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4. Important Relations
– 1/2 = 0.5 = 50%
– 1/3 ≈ 0.333 = 33.33%
– 1/4 = 0.25 = 25%
– 1/5 = 0.2 = 20%
– 1/8 = 0.125 = 12.5%

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5. SSC Exam Tips
– Practice conversions quickly.
– Percent-based questions are common in profit-loss and data interpretation.
– Memorize standard fraction-to-percentage values.

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Example Questions (Solved):
1. Convert 0.375 into fraction and percentage.
Solution:
0.375 = 375/1000 = 3/8
0.375 × 100 = 37.5%

2. If 45% of a number is 180, find the number.
Solution:
45% × X = 180 → X = (180 × 100) / 45 = 400

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✅ Practice Task:
Convert the following:
– 7/20 to percentage
– 0.48 to fraction
– 62.5% to fraction and decimal

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Practice Questions (Unsolved):
Q1. Convert the following:
(a) 35 3/5 into decimal and percentage
(b) 0.875 into fraction and percentage
(c) 45% into fraction and decimal

Q2. A number is 25% of 80. What is the number?

Q3. If a student scored 72 marks out of 120, what is his percentage?

Q4. Increase ₹500 by 12% and decrease ₹800 by 15%.

Q5. Express in descending order: 0.4, 40%, 25 2/5