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

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These are 8 practice questions on Chapter 3, A Peek Beyond the Point, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover comparing lengths in tenths, a two-step problem with litres, what each digit of a decimal stands for, using decimal units, estimating and paying a bill, ordering race times, finding slips in adding decimals, and adding weights to thousandths. 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 no question retells a worked example, exercise or in-text question from the chapter. 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 1, Chapter 3, printed pages 46 to 80):

Tenths, hundredths and place value

Question 1. A tailor has two pieces of lace. One is labelled "58 tenths of a metre" and the other "5 m and 9 tenths of a metre". (a) Which piece is longer, and by how many tenths of a metre? (b) The shorter piece was cut from a roll that held exactly 9 m. How much lace is left on the roll? Give the answer as metres and tenths.

Answer: (a) the 5 m and 9 tenths piece, by 1 tenth of a metre; (b) 3 m and 2 tenths. (a) Write both in tenths. 5 m is 50 tenths, so 5 m and 9 tenths is 50 + 9 = 59 tenths, which is 1 tenth more than 58 tenths. (b) 9 m is 90 tenths, and 90 − 58 = 32 tenths. 32 tenths is 30 tenths and 2 tenths, that is 3 m and 2 tenths (3.2 m). (Units and tenths, and 10 tenths making 1 unit, pages 48 to 51.)

Question 2. A school's water tank can hold 20 litres. In the morning it has 12.75 litres in it. During the day 4.8 litres are used, and then 3.45 litres are poured in. (a) How much water is in the tank now? (b) How much more is needed to fill it?

Answer: (a) 11.4 litres; (b) 8.6 litres. (a) Line up the decimal points and work place by place, as with whole numbers: 12.75 − 4.80 = 7.95, and 7.95 + 3.45 = 11.40 litres, that is 11.4 litres. (b) 20.00 − 11.40 = 8.60 litres, that is 8.6 litres. Check: 11.4 + 8.6 = 20. (Adding and subtracting decimals with the places lined up, page 74.)

Question 3. (a) A packet of rice in a shop is labelled 4.06 kg. What does each of the three digits stand for? Write the weight in grams too. (b) Why is 0.315 read "zero point three one five" and not "zero point three hundred and fifteen"?

Answer: (a) 4 kg, 0 tenths and 6 hundredths of a kg; 4,060 g; (b) because each digit after the point has its own place. (a) The 4 is the whole number part, 4 kg. After the point, the 0 is in the tenths place, so there are no tenths of a kg, and the 6 is in the hundredths place: 6 hundredths of a kg. A hundredth of a kg is 10 g, so 6 hundredths is 60 g, and the packet weighs 4,000 + 60 = 4,060 g. It is not 4,600 g: that would be 4.6 kg. (b) 0.315 means 3 tenths, 1 hundredth and 5 thousandths. The digits after the point are read one by one because each one sits in a different place, so 0.315 is "zero point three one five". (Place value and reading decimals, pages 59 to 63; grams and kilograms, page 67.)

Units, money and comparing

Question 4. (a) A 2 kg bag of sugar is opened, and 3 scoops of 350 g each are taken out. How much sugar is left, in kg? (b) Four pieces, each 28 cm long, are cut from a ribbon 1.5 m long. How much ribbon is left, in m and in cm?

Answer: (a) 0.95 kg; (b) 0.38 m, which is 38 cm. (a) 3 × 350 g = 1,050 g. Since 1 g = 0.001 kg, 1,050 g = 1.05 kg. Left: 2.00 − 1.05 = 0.95 kg (950 g). (b) 4 × 28 cm = 112 cm, and since 1 cm = 0.01 m, 112 cm = 1.12 m. Left: 1.50 − 1.12 = 0.38 m, which is 38 cm. (Units of length and weight in decimals, pages 64 to 68; subtracting decimals, page 74.)

Question 5. A notebook costs ₹38.50, a pen ₹7.75 and an eraser 90 paise. Asha pays with a ₹50 note. (a) Round each price to the nearest whole rupee and add, to get a quick estimate of the bill. (b) Find the exact bill and her change.

Answer: (a) about ₹48; (b) the bill is ₹47.15 and the change is ₹2.85. (a) ₹38.50 rounds to ₹39 (exactly halfway, rounded up), ₹7.75 to ₹8 and 90 paise to ₹1, so the bill is about 39 + 8 + 1 = ₹48. (Rounding to the nearest whole number is from the chapter Large Numbers Around Us, not this one.) (b) 90 paise is ₹0.90. Lining up the points, 38.50 + 7.75 + 0.90 = ₹47.15, close to the estimate. The change is 50.00 − 47.15 = ₹2.85, that is 2 rupees and 85 paise. (Rupees and paise, pages 68 and 69; adding decimals, page 74.)

Question 6. In a 100 m race, four runners' times in seconds are: Anu 12.4, Babli 12.38, Chitra 12.405 and Dimple 12.09. (a) Who won? (b) Put the four in finishing order.

Answer: (a) Dimple; (b) Dimple, Babli, Anu, Chitra. The smallest time wins. All four have 12 whole seconds, so compare place by place from the left. Tenths: Dimple has 0, Babli 3, and Anu and Chitra 4, so Dimple (12.09) is fastest and Babli (12.38) second. Anu's 12.4 is the same as 12.400; against Chitra's 12.405 the tenths and hundredths match, and in the thousandths 0 < 5, so Anu is third and Chitra fourth. Order: 12.09 < 12.38 < 12.4 < 12.405. (Comparing decimals place by place, pages 70 to 73.)

Slips and thousandths

Question 7. Find the slip in each piece of work and correct it. (a) Kiran writes 0.5 + 0.5 = 0.10. (b) Neha adds 2.6 + 1.75 by writing the 6 under the 5, and gets 2.01.

Answer: (a) the sum is 1 (1.0); (b) the sum is 4.35. (a) 0.5 is 5 tenths, and 5 tenths + 5 tenths = 10 tenths, which makes 1 unit, so 0.5 + 0.5 = 1.0. Kiran wrote 10 after the point, but 0.10 is only 1 tenth. (b) Neha lined up the last digits instead of the places, so she really added 0.26 and 1.75. Lining up the points, 2.60 + 1.75 = 4.35. A quick estimate also shows the slip: 2 + 1 = 3, so the answer must be more than 3. (Tenths making a unit, page 48; adding with the places lined up and estimating, pages 74 to 76.)

Question 8. A jeweller weighs three silver rings: 4.125 g, 3.98 g and 4.2 g. (a) Which ring is heaviest? (b) What is their total weight? (c) How much lighter is the lightest ring than the heaviest?

Answer: (a) the 4.2 g ring; (b) 12.305 g; (c) 0.22 g. (a) Write all three to thousandths: 4.125, 3.980 and 4.200. Comparing from the left, 4.200 is the largest, so the 4.2 g ring is heaviest. (b) 4.125 + 3.980 + 4.200 = 12.305 g. (c) The lightest is 3.98 g: 4.200 − 3.980 = 0.220 g, that is 0.22 g. (Thousandths and zeros on the right, pages 61 and 70 to 73; adding and subtracting decimals, page 74.)

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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 + 45 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: A Peek Beyond the Point, Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.