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Class 7 Maths: Another Peek Beyond the Point, 8 practice questions with answers

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These are 8 practice questions on Chapter 4, Another Peek Beyond the Point, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover dividing by 10, 100 and 1000, placing the decimal point in a product, spotting the right product, an electricity bill, prices multiplied by 0.85 and 1.15, long division that ends in decimals, dividing by a decimal (including cutting a rope), divisions that never end, and the leap-year rules with a lunar year. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the chapter's own examples is reused, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 7, Part 2, Chapter 4, printed pages 67 to 96):

Multiplying decimals

Question 1. Find (a) 4.7 ÷ 100, (b) 386 ÷ 1000 and (c) 0.52 ÷ 10. (d) Write 0.047 m in millimetres.

Answer: (a) 0.047; (b) 0.386; (c) 0.052; (d) 47 mm. Move the decimal point one place left for each zero in the divisor, adding zeroes in front when needed. (a) Two places: 4.7 → 0.047. (b) Three places: 386 → 0.386. (c) One place: 0.52 → 0.052. (d) 1 m = 1000 mm, so 0.047 m = 0.047 × 1000 = 47 mm. (Dividing by 10, 100 and 1000, pages 68, 69, 74 and 75.)

Question 2. Three pupils work out 4.37 × 2.6. Arun gets 1.1362, Bela gets 11.362 and Chirag gets 113.62. Who is right? Show how an estimate and a count of decimal places each settle it.

Answer: Bela, 11.362. Estimate: 4.37 is about 4 and 2.6 is about 3, so the product should be about 12. Only 11.362 is close to 12; 1.1362 is far too small and 113.62 far too big. Decimal places: 4.37 has 2 and 2.6 has 1, so the product has 2 + 1 = 3 decimal places, and 437 × 26 = 11362 gives 11.362. Both checks pick Bela's answer. (The rule for multiplying decimals, pages 70 and 71.)

Question 3. A household uses 142.5 units of electricity in a month. Each unit costs ₹6.40, and there is a fixed charge of ₹45.50 on top. The bill is paid with a ₹1000 note. Find the bill and the change.

Answer: the bill is ₹957.50 and the change is ₹42.50. Energy charge: 142.5 × 6.40 = 1425 × 64 thousandths = 91200 thousandths = ₹912.00. Bill: 912.00 + 45.50 = ₹957.50. Change: 1000.00 − 957.50 = ₹42.50. (Multiplying decimals, pages 70 and 71.)

Question 4. A school bag costs ₹480. In a sale its price is multiplied by 0.85, and at another shop a tax makes the price ₹480 × 1.15. Without working them out, which of the two new prices is less than ₹480, and why? Then find both.

Answer: the sale price, ₹408, is less; the price with tax is ₹552. Multiplying by a number less than 1 gives a smaller result, and multiplying by a number greater than 1 gives a larger one. 0.85 is less than 1, so 480 × 0.85 is less than 480; 1.15 is more than 1, so 480 × 1.15 is more than 480. Working them out: 480 × 0.85 = 408 and 480 × 1.15 = 552. (Is the product always greater?, page 72.)

Dividing decimals

Question 5. Find 43 ÷ 16 by long division. Show where the decimal point goes and what is regrouped at each step.

Answer: 2.6875. 43 Ones ÷ 16 gives 2 Ones with 11 Ones left. Regroup the 11 Ones as 110 tenths and put the decimal point in the quotient: 110 ÷ 16 = 6 tenths, 14 tenths left. Regroup as 140 hundredths: 140 ÷ 16 = 8 hundredths, 12 left. Regroup as 120 thousandths: 120 ÷ 16 = 7 thousandths, 8 left. Regroup as 80 ten-thousandths: 80 ÷ 16 = 5, with nothing left. So 43 ÷ 16 = 2.6875. Check with an equivalent fraction: 16 × 625 = 10000, so 43/16 = 26875/10000 = 2.6875. (Division with a decimal quotient, pages 78 to 82.)

Question 6. (a) Find 15.84 ÷ 0.48. (b) A rope 15.6 m long is cut into skipping ropes, each 1.2 m long. How many skipping ropes are made?

Answer: (a) 33; (b) 13. (a) Make the divisor a counting number by multiplying both numbers by 100: 15.84 ÷ 0.48 = 1584 ÷ 48 = 33. Check: 0.48 × 33 = 15.84. (b) The number of pieces is 15.6 ÷ 1.2. Multiply both by 10: 156 ÷ 12 = 13. Check: 1.2 × 13 = 15.6, so nothing is left over. (Division with a decimal divisor, page 84.)

Question 7. Divide (a) 5 by 6 and (b) 7 by 12 by long division. Will either division end? Explain using the remainders.

Answer: (a) 0.8333…; (b) 0.58333…; neither ends. (a) 50 tenths ÷ 6 = 8 with 2 left; 20 hundredths ÷ 6 = 3 with 2 left; and then the remainder is 2 again at every step, so the digit 3 repeats for ever: 5 ÷ 6 = 0.8333… (b) 70 tenths ÷ 12 = 5 with 10 left; 100 hundredths ÷ 12 = 8 with 4 left; 40 ÷ 12 = 3 with 4 left; and then the remainder is 4 at every step, so the digit 3 repeats: 7 ÷ 12 = 0.58333… A division ends only if a remainder of 0 turns up; once a remainder repeats, the same steps repeat. (Divisions that never end, pages 84 to 86.)

Calendar decimals

Question 8. (a) Using the leap-year rules, which of 1900, 2000, 2024 and 2100 are leap years? (b) A lunar month (from one new moon to the next) lasts about 29.53 days. How many days are there in 12 lunar months, and how many days short of a 365-day year is that?

Answer: (a) 2000 and 2024; (b) 354.36 days, which is 10.64 days short of 365. (a) 1900 and 2100 are divisible by 100 but not by 400, so they are not leap years. 2000 is divisible by 400, so it is one. 2024 is divisible by 4 and not by 100, so it is one. (b) 12 × 29.53 = 12 × 2953 hundredths = 35436 hundredths = 354.36 days, and 365 − 354.36 = 10.64 days short. (The length of the lunar month is from outside the chapter.) (Look before you leap, pages 88 to 92; multiplying decimals, pages 70 and 71.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 66 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Another Peek Beyond the Point, Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.