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SBI PO Fractions & Decimals

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This page covers SBI PO Fractions & Decimals with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Fractions & Decimals— Rules & Concept

Core ConceptRead this first — the foundation of the topic

Core Concept: Fractions represent parts of a whole. A fraction has two parts - numerator (top number) and denominator (bottom number). Decimals are another way to write fractions using place values after a decimal point. Both are extensively tested in SSC CGL. **

Key RulesCore rules you must know cold

** Every fraction can be converted to decimal form by dividing numerator by denominator. Terminating decimals have denominators with only factors of 2 and 5. Non-terminating decimals have denominators with factors other than 2 and 5. When adding fractions, find common denominator first.

When multiplying fractions, multiply numerators together and denominators together. **

Formula BlockMemorise — at least one formula appears in every paper

Fraction to Decimal: Numerator ÷ Denominator

Decimal to Fraction: Remove decimal, divide by appropriate power of 10

Addition: a/b + c/d = (ad + bc)/(bd)
Subtraction: a/b - c/d = (ad - bc)/(bd)
Multiplication: a/b × c/d = (ac)/(bd)
Division: a/b ÷ c/d = (ad)/(bc)

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL frequently asks fraction comparisons, decimal conversions, arithmetic operations with mixed numbers, and word problems involving parts of quantities. Questions often involve finding equivalent fractions, simplifying complex fractions, and converting recurring decimals to fractions. Shortcut - Cross Multiplication for Comparison: To compare fractions a/b and c/d, multiply a×d and b×c. If a×d > b×c, then a/b > c/d. This saves time over finding common denominators.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Cross multiply - 7×6 = 42 and 9×5 = 45

2
Step 2

Compare results - 42 < 45

3
Step 3

Therefore 7/9 < 5/6 Converting Recurring Decimal 0.363636... to Fraction:

1
Step 1

Let x = 0.363636...

2
Step 2

Multiply by 100 (since 2 digits repeat): 100x = 36.363636...

3
Step 3

Subtract original: 100x - x = 36

4
Step 4

Solve: 99x = 36, so x = 36/99 = 4/11

5
Step 5

Verify: 4÷11 = 0.363636... ✓ Another Shortcut - Decimal Place Memory: For quick conversions, remember that 1/8 = 0.125, 1/3 = 0.333..., 1/6 = 0.1666..., 1/7 = 0.142857... (repeating). These frequently appear in options. **

Exam TrapsCommon mistakes students make — avoid these

** Students often forget to simplify fractions to lowest terms or make errors with recurring decimals. Always reduce fractions by finding the highest common factor of numerator and denominator. Also, when dealing with mixed numbers, convert to improper fractions first before performing operations.

Key Points to Remember

  • Fraction = Numerator/Denominator represents parts of a whole number
  • Terminating decimals have denominators with only factors 2 and 5
  • Cross multiplication shortcut: a/b vs c/d compare a×d with b×c
  • To add fractions: a/b + c/d = (ad + bc)/(bd)
  • Recurring decimal with n repeating digits: multiply by 10^n then subtract
  • Mixed number operations: convert to improper fractions first
  • Always simplify final answers using HCF of numerator and denominator
  • 1/7 = 0.142857... (6-digit repetition) appears frequently in SSC

Exam-Specific Tips

  • 1/3 = 0.333... (non-terminating recurring decimal)
  • 1/8 = 0.125 (terminating decimal)
  • 1/7 = 0.142857142857... (6-digit recurring pattern)
  • 1/6 = 0.16666... (recurring decimal starting after first digit)
  • 1/11 converts any 2-digit recurring decimal (like 0.363636... = 4/11)
  • Fractions with denominators having prime factors other than 2,5 give non-terminating decimals
  • 1/9 = 0.111..., 2/9 = 0.222..., following pattern up to 8/9 = 0.888...
  • Any decimal with denominator as power of 10 can be directly written as fraction
Practice MCQs

Fractions & Decimals — Practice Questions

6graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

Convert 0.625 to a fraction in its simplest form.

Practice 2easy

If 2/5 of a number is 48, what is the number?

Practice 3easy

If 3/4 of a tank holds 180 litres, how many litres does the full tank hold?

Practice 4medium

A shopkeeper has 3/5 of his stock as rice and 1/4 of the remaining stock as wheat. If the total stock is 800 kg, how many kg of wheat does he have?

Practice 5medium

If 2.5 litres of milk costs ₹62.50, what is the cost of 0.8 litres of milk at the same rate?

Practice 6medium

A number when divided by 2/3 gives 18. What is 1/4 of that number?

60-Second Revision — Fractions & Decimals

  • Remember: Cross multiply to compare fractions quickly without finding LCM
  • Formula: Recurring decimal conversion - multiply by 10^n, subtract, solve
  • Trap: Always check if fraction can be simplified using HCF
  • Quick recall: 1/8=0.125, 1/3=0.333..., 1/7=0.142857..., 1/6=0.1666...
  • Method: Convert mixed numbers to improper fractions before operations
  • Check: Denominators with only factors 2,5 give terminating decimals
  • Shortcut: For addition a/b + c/d use cross multiplication formula (ad+bc)/(bd)
←Number SeriesSimplification & Approximation→
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