RRB NTPC · Bite-size lessons

Decimals and Fractions

About 6 min · Mathematics · English

Time worked out from the lesson's 392 words at 150 words a minute, plus a minute for each question.

Decimals and fractions form the backbone of arithmetic computation in RRB NTPC exams. Mastery here means speed and accuracy — a strong candidate converts between forms instinctively and performs operations without hesitation.

Key ideas

• Fraction representation: A fraction a/b represents division of a by b. The numerator (a) is the part; denominator (b) is the whole. Proper fraction: a < b. Improper fraction: a ≥ b. Mixed number: whole number + proper fraction (e.g., 2 3/4).
• Decimal representation: A decimal is another way to write fractions with denominators 10, 100, 1000, etc. The decimal point separates the whole part (left) from the fractional part (right). Each place to the right is one-tenth of the previous: tenths (0.1), hundredths (0.01), thousandths (0.001).
• Conversion fraction → decimal: Divide numerator by denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Terminating decimals end (like 0.5, 0.125); non-terminating decimals repeat forever (like 1/3 = 0.333...).
• Conversion decimal → fraction: Write the decimal as a fraction with denominator 10, 100, 1000 (depending on decimal places), then simplify. Example: 0.6 = 6/10 = 3/5. For repeating decimals, use the algebraic method.
• Like and unlike fractions: Fractions with the same denominator are like fractions (can add/subtract directly). Unlike fractions need a common denominator first (usually the LCM of denominators).

Watch out for

• Misplacing the decimal point in multiplication/division: Students forget to count total decimal places or shift incorrectly. Fix: Always count decimal places before and after operation; double-check by estimation (e.g., 2.5 × 1.2 should be near 3, not 30).
• Adding/subtracting fractions without common denominator: Directly adding numerators and denominators (e.g., 1/2 + 1/3 ≠ 2/5). Fix: Always find LCM of denominators first, convert both fractions, then add/subtract numerators only.
• Forgetting to simplify final answers: Leaving 4/8 instead of 1/2, or 0.500 instead of 0.5. Fix: Make simplification a reflex — cancel HCF for fractions, drop trailing zeros for decimals.

Quick reference

• Fraction to decimal: divide top by bottom.
• Decimal to fraction: write over power of 10, simplify.
• Add/subtract fractions: common denominator first.
• Multiply fractions: straight across, simplify.
• Divide fractions: multiply by reciprocal.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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