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7. Decimals

CSS GSA — Paper 7, Part-II, Section VI, Sub-topic 7 (Decimals)

Past Paper Weightage

  • Low as a standalone topic, but decimal-fraction-percentage conversion is a recurring building block across quant questions.

Key Concepts

  • Decimal = fraction with denominator a power of 10, written using a decimal point (0.75 = 75/100 = 3/4)
  • Place values right of the decimal: tenths, hundredths, thousandths, ...
  • Addition/Subtraction: align decimal points before operating
  • Multiplication: multiply as whole numbers, then place decimal point so total decimal places in the answer = sum of decimal places in both factors
  • Division: convert divisor to a whole number by shifting the decimal point in both numbers equally, then divide normally
  • Conversions: Fraction → Decimal (divide numerator by denominator); Decimal → Fraction (write over the matching power of 10, simplify); Decimal → Percentage (× 100)

Worked Example

  • 0.25 × 0.4 = 0.1 (2 + 1 = 3 decimal places → 0.100 = 0.1)
  • 3/8 = 0.375

Past Paper Style Numericals (Solved)

  1. A shopkeeper sells cloth at Rs. 45.75 per meter. Find the cost of 8.5 meters.
    • Step 1: Set up the multiplication: 45.75 × 8.5.
    • Step 2: Multiply as whole numbers first: 4575 × 85 = 388,875.
    • Step 3: Count total decimal places in the original numbers (2 + 1 = 3) and place the decimal point accordingly: 388.875 → rounded to Rs. 388.88.
  2. Simplify: 12.6 ÷ 0.3
    • Step 1: To divide by a decimal, shift the decimal point in both numbers until the divisor is a whole number — multiply both by 10.
    • Step 2: This gives 126 ÷ 3.
    • Step 3: Divide: 126 ÷ 3 = 42.
  3. Arrange in ascending order: 0.5, 0.055, 0.55, 0.505
    • Step 1: Line up the decimal points and compare digit by digit: 0.500, 0.055, 0.550, 0.505.
    • Step 2: Compare tenths digits first: 0.055 has 0 tenths (smallest); the rest have 5 tenths, so compare hundredths: 0.500 (0 hundredths), 0.505 (0 hundredths but has a thousandths digit), 0.550 (5 hundredths, largest).
    • Step 3: Ascending order: 0.055 < 0.5 < 0.505 < 0.55.
  4. Convert 0.375 to a fraction in lowest terms.
    • Step 1: Write the decimal over its place-value denominator: 0.375 = 375/1000 (three decimal places = thousandths).
    • Step 2: Find the greatest common divisor of 375 and 1000, which is 125.
    • Step 3: Divide both by 125: 375÷125 = 3, 1000÷125 = 8 → 3/8.

MCQ Traps

  • Recurring/repeating decimals (0.333...) are still rational numbers if the repeat is a fixed pattern — they can be written as fractions
  • Don't forget trailing zeros affect place value alignment in addition, not the value itself

Self-Test Questions

  1. Convert 5/8 to a decimal.
  2. Evaluate: 2.5 × 0.04
  3. Convert 0.625 to a fraction in lowest terms.

Past-Paper MCQs (FPSC)

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

Past-Paper Questions with Answers (FPSC)

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No past paper in the set asked a stand-alone decimals question. Decimals appear inside other questions, such as the fraction ordering below and the cost and probability questions.

  • CSS 2025 Q7(d) (decimal method): Arrange 7/12, 4/7, 9/14, 25/42 in descending order using decimals. (5)
    1. 7 ÷ 12 = 0.583; 4 ÷ 7 = 0.571; 9 ÷ 14 = 0.643; 25 ÷ 42 = 0.595
    2. Order: 0.643 > 0.595 > 0.583 > 0.571
    3. Answer: 9/14 > 25/42 > 7/12 > 4/7
    • Full set of five parts is in the Fractions chapter
  • CSS 2023 Q6(a): A telephone company charges Rs. 0.50 initially and Rs. 0.11 for every minute. Write an expression for the cost of an N-minute call. (5)
    1. Fixed charge = 0.50
    2. Per-minute charge for N minutes = 0.11 × N
    3. Cost = 0.50 + 0.11N rupees (e.g. N = 10 gives Rs. 1.60)

CSS Exam Perspective

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  • How decimals are tested: inside fractions, money and percentage problems rather than on their own
  • Tip: keep money to 2 decimal places and line up decimal points when adding