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14. Rounding Numbers

CSS GSA — Paper 7, Part-II, Section VI, Sub-topic 14 (Rounding Numbers)

Past Paper Weightage

  • Low standalone frequency, but rounding/estimation errors commonly cost marks in multi-step word problems — quick review recommended.

Key Rules

  • Identify the digit at the place value you're rounding to
  • Look at the digit immediately to its right: 5 or more → round up; 4 or less → round down (stays the same)
  • All digits after the rounding place become 0 (for whole numbers) or are dropped (for decimals)
  • Significant figures: all digits that carry meaningful precision (non-zero digits are always significant; zeros between non-zero digits are significant; leading zeros are not)
  • Estimation: rounding values before a calculation to quickly approximate an answer — useful for sanity-checking exam calculations under time pressure

Worked Example

  • Round 4,567 to the nearest hundred → 4,600
  • Round 3.14159 to 2 decimal places → 3.14
  • Round 149 to the nearest ten → 150

Past Paper Style Numericals (Solved)

  1. Round 6,782,459 to the nearest lakh (100,000).

    Answer: 6,800,000

  2. A bill of Rs. 1,247.60 is rounded to the nearest rupee. What is the rounded amount?

    Answer: Rs. 1,248

  3. Estimate the product 812 × 49 by rounding to the nearest ten/hundred, then compare to the exact value.

    Answer: estimate ≈ 800×50 = 40,000; exact = 39,788

MCQ Traps

  • Rounding "5" up is the standard convention tested (some banking/statistical contexts round-half-to-even, but CSS-level questions use standard round-half-up)
  • Rounding at intermediate steps in a multi-step problem can shift the final answer — round only the final result unless instructed otherwise

Self-Test Questions

  1. Round 28,451 to the nearest thousand.
  2. Round 0.0876 to 3 decimal places.
  3. Estimate 397 × 21 by rounding each number first, then compute the exact answer and compare.

Past-Paper MCQs (FPSC)

✅

The FPSC MCQ papers you shared (2024 and 2025) had no direct rounding question.

Past-Paper Questions with Answers (FPSC)

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No past paper in the set asked a stand-alone rounding question; rounding is used to finish other answers.

  • Where rounding was needed in past answers
    • CSS 2024 Q8(c): D = 2,000 ÷ 90 = 22.222… → 22.22 m (2 decimal places)
    • CSS 2023 Q7(a): 11.18 + 1.5 = 12.68 m
    • CSS 2020 Q8(c): 2,000 ÷ 70 = 28.57 → 28.6 days (1 decimal place)
    • CSS 2020 Q6(a): 4/7 hour = 34.3 minutes → about 34 minutes
    • Rule: look at the next digit; 5 or more rounds up, 4 or less leaves the digit as it is

CSS Exam Perspective

🎯

  • How rounding is tested: as the last step of word problems, so give answers to the precision the question implies
  • Tip: keep full values during the working and round only at the end