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03
NCERT Solutions · Maths Ch 3
A Peek Beyond the Point
42 questions · 4 exercises
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Ex 3.1
Ex 3.2
Ex 3.3
Ex 3.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 3.1 · 8 QUESTIONS
Tenths and Hundredths of a Unit
Q1
Arrange the lengths in increasing order: (a) 9/10 (b) 1 7/10 (c) 130/10 (d) 13 1/10 (e) 10 5/10 (f) 7 6/10 (g) 6 7/10 (h) 4/10
(3 marks)
Q2
Arrange the following lengths in increasing order: 4 1/10, 4/10, 41/10, 41 1/10
(2 marks)
Q3
The lengths of the body parts of a honeybee are: Head = 2 3/10 units, Thorax = 5 4/10 units, Abdomen = 7 5/10 units. Find its total length.
(3 marks)
Q4
A Celestial Pearl Danio's length is 2 4/10 cm and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?
(2 marks)
Q5
Observe the given sequences, identify the change after each term and extend the pattern by four terms: (a) 4, 4 3/10, 4 6/10, … (b) 8 2/10, 8 7/10, 9 2/10, … (c) 7 6/10, 8 7/10, … (d) 5 7/10, 5 3/10, … (e) 13 5/10, 13, 12 5/10, … (f) 11 5/10, 10 4/10, 9 3/10, …
(5 marks)
Q6
How many one-hundredths make one-tenth? Can we also say that a length is 4 units and 45 one-hundredths?
(2 marks)
Q7
For the lengths shown on the scale, write the measurements and read them in words: (i) 5 37/100 (ii) 15 3/100 (iii) 7 52/100 (iv) 9 80/100
(2 marks)
Q8
In each group, identify the longest and the shortest lengths: (a) 3/10, 3/100, 33/100 (b) 3 1/10, 30/10, 1 3/10 (c) 45/100, 54/100, 5/10, 4/10 (d) 3 6/10, 3 6/100, 3 6/10 6/100 (e) 8/10 2/100, 9/100, 1 8/100 (f) 7 3/10 5/100, 7 5/10, 7 41/100 (g) 6 5/10 15/100, 5 87/100, 5 7/100
(3 marks)
2
EXERCISE 3.2 · 13 QUESTIONS
Decimal Place Value
Q9
Find the sums and differences: (a) 3/10 + 3 4/100 (b) 9 5/10 7/100 + 2 1/10 3/100 (c) 15 6/10 4/100 + 14 3/10 6/100 (d) 7 7/100 − 4 4/100 (e) 8 6/100 − 5 3/100 (f) 12 6/10 2/100 − 9/10 9/100
(5 marks)
Q10
Make a place value table. Write each quantity in decimal form and read the number: (a) 2 ones, 3 tenths and 5 hundredths (b) 1 ten and 5 tenths (c) 4 ones and 6 hundredths (d) 1 hundred, 1 one and 1 hundredth (e) 98/100 as 9/10 and 8/100 (f) 5/100 (g) 1/10 (h) 2 ones and 1/100; 4 ones and 1/10; 7 ones and 7/1000; 13 ones, 1/10, 1/100, 7/1000
(5 marks)
Q11
Write these quantities in decimal form: (a) 234 hundredths (b) 105 tenths
(2 marks)
Q12
Fill in the blanks (mm ↔ cm): 12 mm = __ cm, 56 mm = __ cm, 70 mm = __ cm, 9 mm = __ cm, 134 mm = __ cm, 2036 mm = __ cm
(2 marks)
Q13
Fill in the blanks (cm ↔ m): 36 cm, 50 cm, 89 cm, 4 cm, 325 cm, 207 cm. How many mm does 1 metre have? Can we write 1 mm = 1/1000 m?
(3 marks)
Q14
Fill in the blanks (g ↔ kg): 465 g, 68 g, 1560 g, 704 g, 560 g, 2500 g
(2 marks)
Q15
Fill in the blanks (paise ↔ rupee): 10 p, 5 p, 36 p, 50 p, 99 p, 250 p
(2 marks)
Q16
Name all the divisions between 1 and 1.1 on the number line. Identify and write the decimal numbers against the letters d and e (8 to 8.1 divided into 10 equal parts, d at the first division and e at the fifth).
(3 marks)
Q17
Which of these is the smallest and which is the largest: 0.2, 0.20, 0.200, 0.02, 0.002? Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
(5 marks)
Q18
In the number line below (5 to 10, with 10 equal divisions), what decimal numbers do the boxes labelled a, b and c denote? (b is 7.5.)
(3 marks)
Q19
Which decimal number is greater? (a) 1.23 or 1.32 (b) 3.81 or 13.800 (c) 1.009 or 1.090
(3 marks)
Q20
(a) Which of 0.9, 1.1, 1.01, 1.11 is closest to 1.09? (b) Which among 3.56, 3.65, 3.099 is closest to 4? (c) Which among 0.8, 0.69, 1.08 is closest to 1?
(3 marks)
Q21
Use the digits 4, 1, 8, 2 and 5 exactly once to make a decimal number as close as possible to 25.
(2 marks)
3
EXERCISE 3.3 · 5 QUESTIONS
Decimal Sums, Differences and Sequences
Q22
Find the sums: (a) 5.3 + 2.6 (b) 18 + 8.8 (c) 2.15 + 5.26 (d) 9.01 + 9.10 (e) 29.19 + 9.91 (f) 0.934 + 0.6 (g) 0.75 + 0.03 (h) 6.236 + 0.487
(5 marks)
Q23
Find the differences: (a) 5.6 − 2.3 (b) 18 − 8.8 (c) 10.4 − 4.5 (d) 17 − 16.198 (e) 17 − 0.05 (f) 34.505 − 18.1 (g) 9.9 − 9.09 (h) 6.236 − 0.487
(5 marks)
Q24
Observe the decimal sequence 4.4, 4.8, 5.2, 5.6, 6.0, … Identify the change and write the next 3 terms.
(2 marks)
Q25
Identify the change and write the next 3 terms: (a) 4.4, 4.45, 4.5, … (b) 25.75, 26.25, 26.75, … (c) 10.56, 10.67, 10.78, … (d) 13.5, 16, 18.5, … (e) 8.5, 9.4, 10.3, … (f) 5, 4.95, 4.90, … (g) 12.45, 11.95, 11.45, … (h) 36.5, 33, 29.5, …
(5 marks)
Q26
Sonu says: 'If we add two decimal numbers, the sum will always be greater than the sum of their whole number parts and less than 2 more than the sum of their whole number parts.' Verify this for 25.936 and 8.202. Will it work for any 2 decimal numbers?
(3 marks)
4
16 QUESTIONS
Exercise 3.4
Q27
Convert the following fractions into decimals: (a) 5/100 (b) 16/1000 (c) 12/10 (d) 254/1000
(2 marks)
Q28
Convert the following decimals into a sum of tenths, hundredths and thousandths: (a) 0.34 (b) 1.02 (c) 0.8 (d) 0.362
(2 marks)
Q29
What decimal number does each letter represent on the number line (6.4, 6.5, 6.6 marked; between 6.4 and 6.5 there are 3 small marks, and the same between 6.5 and 6.6)? Letters a, c and b point to the second mark after 6.4, the first mark after 6.5 and the second mark after 6.5.
(3 marks)
Q30
Arrange the following quantities in descending order: (a) 11.01, 1.011, 1.101, 11.10, 1.01 (b) 2.567, 2.675, 2.768, 2.499, 2.698 (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m
(3 marks)
Q31
Using the digits 1, 4, 0, 8 and 6 make: (a) the decimal number closest to 30 (b) the smallest possible decimal number between 100 and 1000.
(3 marks)
Q32
Will a decimal number with more digits be greater than a decimal number with fewer digits?
(2 marks)
Q33
Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums and 0.05 kg of ginger. Calculate the total weight of the items she bought.
(2 marks)
Q34
Pinto supplies 3.79 L, 4.2 L and 4.25 L of milk to a milk dairy in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity of milk supplied in the last three days.
(2 marks)
Q35
Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
(2 marks)
Q36
Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ____, ____
(3 marks)
Q37
How many millimetres make 1 kilometre?
(2 marks)
Q38
Indian Railways offers optional travel insurance for e-tickets at 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
(2 marks)
Q39
Which is greater? (a) 10/1000 or 1/10 (b) One-hundredth or 90 thousandths (c) One-thousandth or 90 hundredths
(3 marks)
Q40
Write the decimal forms of the quantities: (a) 87 ones, 5 tenths and 60 hundredths (b) 12 tens and 12 tenths (c) 10 tens, 10 ones, 10 tenths and 10 hundredths (d) 25 tens, 25 ones, 25 tenths and 25 hundredths
(5 marks)
Q41
Using each digit 0–9 not more than once, fill the boxes (a number with one digit before and three after the decimal point, plus another such number) so that the sum is closest to 10.5.
(2 marks)
Q42
Write the following fractions in decimal form: (a) 1/2 (b) 3/2 (c) 1/4 (d) 3/4 (e) 1/5 (f) 4/5
(3 marks)