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12
NCERT Solutions · Maths Ch 12
Another Peek Beyond the Point
36 questions · 3 exercises
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Ex 12.1
Ex 12.2
Ex 12.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 12.1 · 10 QUESTIONS
Decimal Multiplication
Q1
Recall that a tenth is 0.1, a hundredth is 0.01, and so on. Find the following products in tenths, hundredths and so on: (a) 6 × 4 tenths = 24 tenths (b) 7 × 0.3 (c) 9 × 5 hundredths
(3 marks)
Q2
Find the products: (a) 27.34 × 6 (b) 4.23 × 3.7 (c) 0.432 × 0.23
(5 marks)
Q3
Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts?
(2 marks)
Q4
Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹15.50 and each eraser was ₹2.75. How much did she spend in all?
(2 marks)
Q5
The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by placing 36 rupee coins one over the other? Write the answer in centimetres.
(2 marks)
Q6
The price of 1 kg of oranges is ₹56.50. What is the price of 2.250 kg of oranges? Can we write 56.50 as 56.5 and 2.250 as 2.25 and multiply? Will we get the same product? Why?
(3 marks)
Q7
Dwarakanath purchases notebooks at a wholesale price of ₹23.6 per piece and sells each notebook at ₹30. How much profit does he make if he sells 50 books in a week?
(3 marks)
Q8
Given that 18 × 12 = 216, find the products: (a) 18 × 1.2 (b) 18 × 0.12 (c) 1.8 × 1.2 (d) 0.18 × 0.12 (e) 0.018 × 0.012 (f) 1.8 × 12. In which of the cases above is the product less than 1?
(3 marks)
Q9
In which of the following multiplications is the product less than 1? Can you find the answer without actually doing the multiplications? (a) 7 × 0.6 (b) 0.7 × 0.6 (c) 0.7 × 6 (d) 0.07 × 0.06
(2 marks)
Q10
Multiply the following numbers by 10, 100 and 1000 to complete the table: 5.7, 23.02, 0.92, 0.306, 24.67
(3 marks)
2
EXERCISE 12.2 · 15 QUESTIONS
Decimal Division
Q11
Find the quotient by converting the denominator into 1, 10, 100 or 1000 and verify the solution by the long division method (division by place value): (a) 18/5 (b) 415/4 (c) 1217/2 (d) 4827/8
(5 marks)
Q12
Choose the correct answer: (a) 1526/4 = (i) 38.15 (ii) 380.15 (iii) 381.5 (iv) 381.05 (b) 3567/8 = (i) 4458.75 (ii) 44.5875 (iii) 445.875 (iv) 4458.75
(5 marks)
Q13
What is the quotient? (a) 132 ÷ 4 (b) 13.2 ÷ 4 (c) 1.32 ÷ 4 (d) 0.132 ÷ 4
(3 marks)
Q14
What is the quotient? (a) 126 ÷ 8 (b) 12.6 ÷ 8 (c) 1.26 ÷ 8 (d) 0.126 ÷ 8 (e) 0.0126 ÷ 8
(3 marks)
Q15
Express the following fractions in decimal form: (a) 2/5 (b) 13/4 (c) 4/50 (d) 5/8
(3 marks)
Q16
Find the quotients: (a) 24.86 ÷ 1.2 (b) 5.728 ÷ 1.52
(5 marks)
Q17
Evaluate using the information 156 × 12 = 1872: (a) 15.6 × 1.2 (b) 187.2 ÷ 1.2 (c) 18.72 ÷ 15.6 (d) 0.156 × 0.12
(3 marks)
Q18
Evaluate: (a) 25 ÷ ____ = 0.025 (b) 25 ÷ ____ = 250 (c) 25 ÷ ____ = 2.5 (d) 25 ÷ 10 = 25 × ____ (e) 25 ÷ 0.10 = 25 × ____ (f) 25 ÷ 0.01 = 25 × ____
(3 marks)
Q19
Find the quotient: (a) 2.46 ÷ 1.5 (b) 2.46 ÷ 0.15 (c) 2.46 ÷ 0.015. Is the quotient obtained in 24.6 ÷ 1.5 the same as the quotient obtained in 2.46 ÷ 0.15?
(5 marks)
Q20
A 4 m long wooden block has to be cut into 5 pieces of equal length. What is the length of each piece?
(2 marks)
Q21
If the perimeter of a regular polygon with 12 sides is 208.8 cm, what is the length of its side?
(2 marks)
Q22
3 litres of watermelon juice is shared among 8 friends equally. How much watermelon juice will each get? Express the quantity of juice in millilitres.
(3 marks)
Q23
A car covers 234.45 km using 12.6 litres of petrol. What is the distance travelled per litre?
(2 marks)
Q24
13.5 kg of flour (aata) was distributed equally among 15 students. How much flour did each student receive?
(2 marks)
Q25
Look at the pattern: 1/2 = 0.5, 1/(2×2) = 0.25, 1/(2×2×2) = 0.125, 1/(2×2×2×2) = 0.0625, and 1/5 = 0.2, 1/(5×5) = 0.04, 1/(5×5×5) = 0.008, 1/(5×5×5×5) = 0.0016. Find 1/(2×2×2×2×2) and 1/(5×5×5×5×5). What pattern do you observe? Why are 2 and 5 related in this way?
(3 marks)
3
EXERCISE 12.3 · 11 QUESTIONS
End of Chapter
Q26
Given that 756 ÷ 36 = 21, find the following quotients: (a) 75.6 ÷ 3.6 (b) 7.56 ÷ 0.36 (c) 756 ÷ 0.36 (d) 75.6 ÷ 360 (e) 7560 ÷ 3.6 (f) 7.56 ÷ 0.36
(5 marks)
Q27
A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper?
(2 marks)
Q28
Write the decimal number at the arrow mark: (Figure: a number line from 3.1 to 3.2 divided into 10 equal parts with the arrow at the 6th mark; and a number line from 2.15 to 2.17 divided into 10 equal parts with the arrow at the 6th mark.)
(5 marks)
Q29
Shyamala bought 3 kg bananas at ₹30 per kg. She counted 35 bananas in all. She sells each banana for ₹5. How much profit does she make selling all the bananas?
(2 marks)
Q30
A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long. How many books could be placed on the shelf? Was there any space left? If yes, how much?
(3 marks)
Q31
Fill in the following blanks appropriately: 5.5 km = ____ m; 35 cm = ____ m; 14.5 cm = ____ mm; 68 g = ____ kg; 9.02 m = ____ mm; 125.5 ml = ____ l (Given: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 g = 1000 mg, 1 l = 1000 ml)
(3 marks)
Q32
Sridharacharya (Patiganita): '6¼ is divided by 2½, and 60¼ is divided by 3½. Tell the quotients separately.' Try to solve it by converting the fractions into decimals.
(5 marks)
Q33
Fill the boxes in at least 2 different ways: (a) ☐ × ☐ = 2.4 (b) ☐ × ☐ = 14.5
(3 marks)
Q34
Find the missing cells if each cell represents a ÷ b. Row b: 37, 3.7, 0.37, 0.037, 370; column a: 1517, 151.7, 15.17, 1.517, 15170. (Given: 1517 ÷ 37 = 41; 15.17 ÷ 3.7 = 4.1; 151.7 ÷ 0.037 = 4100.)
(3 marks)
Q35
Using the digits 2, 4, 5, 8 and 0, fill the boxes in ☐☐.☐ × ☐.☐ to get: (a) the maximum product (b) the minimum product (c) a product greater than 150 (d) a product nearest to 100 (e) a product nearest to 5
(3 marks)
Q36
Sort the following expressions in increasing order: (a) 245.05 × 0.942368 (b) 245.05 × 7.9682 (c) 245.05 ÷ 7.9682 (d) 245.05 ÷ 0.942368 (e) 245.05 (f) 7.9682
(5 marks)