Exercise 1.3 — Decimal Representation

Exercise 1.3 — Decimal Form of Rational Numbers

Every rational number p/q has either a terminating or a non-terminating recurring decimal form. Exercise 1.3 in Class 8 Mathematics teaches you to predict which type a fraction will produce and to convert between fraction and decimal representations — a topic that directly precedes irrational numbers in Class 9.

The Terminating vs Recurring Rule

• p/q (in lowest terms) terminates if and only if q = 2^m × 5^n for non-negative integers m, n — check prime factorisation of q first.
• If q has any prime factor other than 2 or 5, the decimal is non-terminating recurring.
• To convert a recurring decimal x = 0.ā₁ā₂...āₙ to fraction: multiply by 10^n, subtract x, solve — works every time.
• Performing +/− on decimals: convert both to same decimal places first; for ×, count total decimal places in the result.
• Always verify by converting your fraction answer back to decimal form.

Exam Frequency

Decimal representation is a guaranteed topic in CBSE, Telangana and Andhra Pradesh Class 8 examinations. 1-mark questions ask whether a fraction terminates; 2-mark questions ask for the decimal form; 3-mark questions ask for conversion of recurring decimals to fractions. Master all three levels before your board exam.

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