RRB Group D · Bite-size lessons

Decimals and Fractions

About 6 min · Mathematics · English

Time worked out from the lesson's 376 words at 150 words a minute, plus a minute for each question.

Decimals and fractions form the backbone of numerical computation in Railway Group D exams. Almost every arithmetic topic — percentage, ratio, profit-loss, time-work — requires fluent conversion between these forms and accurate computation.

Key ideas

• Fraction basics: A fraction a/b has numerator a and denominator b (b ≠ 0). Proper fraction: a < b. Improper fraction: a ≥ b. Mixed number: whole number plus proper fraction (e.g. 2 3/5).
• Decimal place value: In 12.345, 3 is tenths (1/10), 4 is hundredths (1/100), 5 is thousandths (1/1000). Every decimal is implicitly a fraction with denominator 10, 100, 1000, etc.
• Like and unlike fractions: Like fractions share the same denominator (1/7, 3/7). Unlike fractions have different denominators (1/3, 2/5) and require LCM to add or subtract.
• Equivalent fractions: Multiplying or dividing numerator and denominator by the same non-zero number yields an equivalent fraction. 2/3 = 4/6 = 6/9.
• Terminating vs recurring decimals: Fraction converts to terminating decimal if denominator (in lowest terms) has only factors 2 and/or 5. Otherwise recurring: 1/3 = 0.333..., written 0.3̅.

Watch out for

• Forgetting to align decimal points in addition/subtraction → Always write numbers one below the other with decimal points in a vertical line. Treat absent digits as zeros: 3.4 + 0.567 should be aligned as 3.400 + 0.567.
• Adding denominators when adding fractions → Never do (a/b) + (c/d) = (a+c)/(b+d). Correct method: find common denominator using LCM, convert, then add numerators only.
• Placing decimal incorrectly in multiplication → Count total decimal places in both factors combined, not in each separately. 1.2 × 0.3: total 2 places, so 36 becomes 0.36, not 0.036.

Quick reference

• Decimal ↔ Fraction: 0.25 = 1/4, 0.5 = 1/2, 0.75 = 3/4, 0.2 = 1/5, 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8.
• Recurring shortcut: 0.3̅ = 1/3, 0.6̅ = 2/3, 0.1̅ = 1/9, 0.16̅ = 1/6.
• Mixed ↔ Improper: 3 1/4 = 13/4; 22/7 = 3 1/7.
• Fraction division = multiply by reciprocal: a/b ÷ c/d = a/b × d/c.
• LCM method for addition: Convert unlike fractions to like fractions using LCM of denominators, then add/subtract.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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