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Class 7 Mathematics Chapter 4 Worksheet: Another Peek Beyond the Point

Updated:6 Mins Read

Here is a worksheet from Ganita Prakash, grade 7, Part II. The chapter is “Another Peek Beyond the Point,” which is all about decimal multiplication & division. Attempt the questions in order as given below. Use estimation to give the final answer when the decimal places exceed 3-4.

Class 7 Mathematics – Another Peek Beyond the Point (Decimals: Multiplication & Division)

A. Quick Recap of Decimals (Place Value + Conversions)

  1. Jonali says a fraction. Pallabi gives the equivalent decimal. Write Pallabi’s answers:

    1. 7/10
    2. 43/100
    3. 509/1000
    4. 83/10000
  2. Jonali bought spices: 50 g cinnamon, 100 g cumin, 25 g cardamom, 250 g pepper.
    Convert each into kilograms and write it in:

    1. fraction form
    2. decimal form
  3. Write each fraction as a sum of fractions and also as a decimal:

    1. 847/10000
    2. 173/100
    3. 23/1000
  4. Without long division, find:

    1. 123 ÷ 10
    2. 24 ÷ 100
    3. 678 ÷ 1000
    4. 12 ÷ 1000
    5. 12345 ÷ 1000

B. Decimal Multiplication (Place the Decimal Like a Pro)

  1. You know that 596 × 248 = 147808. Without doing full multiplication again, find:

    5.96 × 24.8 = ?
  2. Ajay’s school is 827 m from his home. He walks to school and back home, 6 days a week.
    Find how much he walks in a week in kilometres.
  3. Find the area of a rectangle of sides 5.7 cm and 13.3 cm.
    (Answer in square centimetres.)
  4. Multiply:

    1. 12.5 × 7.5
    2. 9.5 × 5
    3. 1.64 × 6
  5. Multiply and check using estimation (roughly):

    1. 0.48 × 3.5
    2. 2.04 × 0.6
    3. 0.125 × 32
  6. “Can the product of two decimals be a natural number?”

    Give:

    1. One example where the product is a natural number
    2. One example where the product is not a natural number

C. Division Using Place Value (Long Division, but With Decimals)

  1. Find 237 ÷ 8.
  2. A shopkeeper has 9.5 kg sugar and packs it equally in 4 bags.
    What is the weight of sugar in each bag?
  3. Divide:

    1. 72.6 ÷ 6
    2. 5.04 ÷ 8
    3. 3.75 ÷ 15
  4. Concept check (no calculation needed):

    While doing long division of decimals, when exactly do we place the decimal point in the quotient?
    Write the rule in one clear sentence.

D. Division with a Decimal Divisor (Make the Divisor a Whole Number)

  1. Ravi travelled 126 km in 2.5 hours on a scooter.
    Find his average speed (in km/h).
  2. Find 4.68 ÷ 1.3.
  3. Find 4.68 ÷ 0.13.
  4. Compare and explain in 1–2 lines:

    Which is larger: 4.68 ÷ 0.13 or 4.68 ÷ 1.3? Why?

E. Does This Ever End? (Non-Terminating Division)

  1. Find 10 ÷ 3 up to 4 decimal places.
    Also state what remainder keeps repeating at each step.
  2. Challenge:

    Write 1 ÷ 7 as a decimal up to 6 decimal places.
    Then write one sentence describing what kind of decimal it is (terminating / non-terminating repeating / non-terminating non-repeating).

Answer Key with Hints (How to Think, Not Just What to Write)

A. Quick Recap

  1. Answers:

    1. 7/10 = 0.7
    2. 43/100 = 0.43
    3. 509/1000 = 0.509
    4. 83/10000 = 0.0083

    Hint: Denominator tells the place value (10 → tenths, 100 → hundredths, 1000 → thousandths, 10000 → ten-thousandths).

  2. Answers:

    1. 50 g = 50/1000 kg = 0.05 kg
    2. 100 g = 100/1000 kg = 0.1 kg
    3. 25 g = 25/1000 kg = 0.025 kg
    4. 250 g = 250/1000 kg = 0.25 kg

    Hint: 1 kg = 1000 g, so divide grams by 1000 (move decimal 3 places left).

  3. Answers:

    1. 847/10000 = 800/10000 + 40/10000 + 7/10000 = 0.0847
    2. 173/100 = 100/100 + 70/100 + 3/100 = 1.73
    3. 23/1000 = 20/1000 + 3/1000 = 0.023

    Hint: Expand the numerator using place value (hundreds/tens/ones) and then convert.

  4. Answers:

    1. 123 ÷ 10 = 12.3
    2. 24 ÷ 100 = 0.24
    3. 678 ÷ 1000 = 0.678
    4. 12 ÷ 1000 = 0.012
    5. 12345 ÷ 1000 = 12.345

    Hint: Divide by 10, 100, 1000 → move decimal left by 1, 2, 3 places respectively.

B. Decimal Multiplication

  1. Answer: 5.96 × 24.8 = 147.808

    Hint: Multiply as whole numbers: 596 × 248 = 147808. Total decimal places = 2 + 1 = 3, so place decimal 3 digits from the right.
  2. Answer: 9.924 km

    Hint: 827 m = 0.827 km. Daily walk = 0.827 × 2. Weekly = (0.827 × 2) × 6.
  3. Answer: 75.81 cm²

    Hint: Multiply 5.7 × 13.3. Total decimal places = 1 + 1 = 2 in the final product.
  4. Answers:

    1. 12.5 × 7.5 = 93.75
    2. 9.5 × 5 = 47.5
    3. 1.64 × 6 = 9.84

    Hint: Multiply as whole numbers, then place decimal using “total decimal digits” rule.

  5. Answers:

    1. 0.48 × 3.5 = 1.68
    2. 2.04 × 0.6 = 1.224
    3. 0.125 × 32 = 4

    Hint: Estimation check: 0.48×3.5 ≈ 0.5×3.5 = 1.75 (close). Also, 0.125 = 1/8, so 32×(1/8)=4.

  6. Sample Answers:

    1. Natural number product: 0.5 × 2.0 = 1
    2. Not a natural number: 0.2 × 0.5 = 0.1

    Hint: A decimal can represent a fraction. Sometimes fractions multiply to a whole number, sometimes they don’t.

C. Division Using Place Value

  1. Answer: 237 ÷ 8 = 29.625

    Hint: Do long division. When you regroup Ones into Tenths, place the decimal point in the quotient and continue with tenths/hundredths/thousandths.
  2. Answer: 9.5 ÷ 4 = 2.375 kg

    Hint: Start with 9 ÷ 4, then carry remainder into tenths. Place decimal before dividing tenths.
  3. Answers:

    1. 72.6 ÷ 6 = 12.1
    2. 5.04 ÷ 8 = 0.63
    3. 3.75 ÷ 15 = 0.25

    Hint: If stuck, remove the decimal temporarily by thinking in fractions (e.g., 5.04 = 504/100).

  4. Answer (Rule): We place the decimal point in the quotient when Ones are regrouped into Tenths.

    Hint: This is the “bridge” from whole-number division to decimal division—after Ones, the next place is Tenths.

D. Division with a Decimal Divisor

  1. Answer: Average speed = 126 ÷ 2.5 = 50.4 km/h

    Hint: Make divisor a whole number: 126 ÷ 2.5 = 1260 ÷ 25.
  2. Answer: 4.68 ÷ 1.3 = 3.6

    Hint: Multiply both by 10: 4.68 ÷ 1.3 = 46.8 ÷ 13.
  3. Answer: 4.68 ÷ 0.13 = 36

    Hint: Multiply both by 100: 4.68 ÷ 0.13 = 468 ÷ 13.
  4. Answer: 4.68 ÷ 0.13 is larger.

    Why: Dividing by a smaller number gives a larger quotient. Here, 0.13 is smaller than 1.3, so the quotient becomes bigger.

    Hint: Compare results from Q16 and Q17: 3.6 vs 36.

E. Does This Ever End?

  1. Answer: 10 ÷ 3 = 3.3333 (up to 4 decimal places)

    Remainder pattern: Remainder stays 1 at each step.

    Hint: In long division, 10 Ones ÷ 3 gives remainder 1, then 10 Tenths ÷ 3 again remainder 1, and it repeats.
  2. Answer: 1 ÷ 7 = 0.142857 (up to 6 decimal places)

    Type: Non-terminating repeating decimal

    Hint: Do long division or remember that the block 142857 repeats for 1/7.

Other Class 7 Maths worksheet

Amit, a BE in Mechanical Engineering, is a math enthusiast dedicated to making math fun and accessible for kids in classes 1 to 10. With a knack for simplifying complex concepts, Amit offers easy-to-understand solutions, fostering a love for math in young minds across India.

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