Figure it Out - 3.1 (Page 148)
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1. A Celestial Pearl Danio's length is 2 cm, and the length of a Philippine Goby is 0.9 cm. What is the difference in their lengths?
$2 - 0.9 = 1.1$ cm
The difference in their lengths is 1.1 cm. -
3. Observe the given sequences of numbers. Identify the change after each term and extend the pattern:
(a) $4\frac{3}{10}, 4\frac{6}{10}, \dots$ $4\frac{9}{10}, 5\frac{2}{10}, 5\frac{5}{10}$
(b) $8\frac{2}{10}, 8\frac{7}{10}, 9\frac{2}{10}, \dots$ $9\frac{7}{10}, 10\frac{2}{10}, 10\frac{7}{10}$
(c) $7\frac{6}{10}, 8\frac{7}{10}, \dots$ $9\frac{8}{10}, 10\frac{9}{10}, 12$
(d) $5\frac{7}{10}, 5\frac{3}{10}, \dots$ $4\frac{9}{10}, 4\frac{5}{10}, 4\frac{1}{10}$
(e) $13\frac{5}{10}, 12\frac{5}{10}, \dots$ $11\frac{5}{10}, 10\frac{5}{10}, 9\frac{5}{10}$
(f) $11\frac{5}{10}, 10\frac{4}{10}, 9\frac{3}{10}, \dots$ $8\frac{2}{10}, 7\frac{1}{10}, 6$
Figure it Out - 3.2 (Pages 152-155)
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1. Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.
$\frac{3}{10}, \frac{30}{100}, \frac{4}{10}, \frac{40}{100}, 1\frac{1}{10}, \frac{110}{100}$
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2. For the lengths shown below write the measurements and read out the measures in words.
(a) Measurement: $5$ units | Words: Five
(b) Measurement: $15$ units | Words: Fifteen
(c) Measurement: $7\frac{5}{10}$ units | Words: Seven and five-tenths
(d) Measurement: $9\frac{8}{10}$ units | Words: Nine and eight-tenths -
3. In each group, identify the longest and the shortest lengths. Mark each length on the scale.
(a) $\frac{3}{10}, \frac{3}{100}, \frac{33}{100}$
Longest: $\frac{33}{100}$, Shortest: $\frac{3}{100}$
(b) $3\frac{1}{10}, \frac{30}{10}, 1\frac{3}{10}$
Longest: $3\frac{1}{10}$, Shortest: $1\frac{3}{10}$
(c) $\frac{45}{100}, \frac{54}{100}, \frac{5}{10}, \frac{4}{10}$
Longest: $\frac{54}{100}$, Shortest: $\frac{4}{10}$
(d) $3\frac{6}{10}, 3\frac{6}{100}, 3\frac{6}{10}\frac{6}{100}$
Longest: $3\frac{6}{10}\frac{6}{100}$, Shortest: $3\frac{6}{100}$
(e) $\frac{8}{10}, \frac{2}{100}, \frac{9}{100}, 1\frac{8}{100}$
Longest: $1\frac{8}{100}$, Shortest: $\frac{2}{100}$
(f) $7\frac{3}{10}\frac{5}{100}, 7\frac{5}{10}, 7\frac{41}{100}$
Longest: $7\frac{5}{10}$, Shortest: $7\frac{3}{10}\frac{5}{100}$
(g) $\frac{65}{10}\frac{15}{100}, 5\frac{87}{100}, 5\frac{7}{100}$
Longest: $\frac{65}{10}\frac{15}{100}$, Shortest: $5\frac{7}{100}$
Figure it Out - 3.3 (Page 160)
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Find the sums and differences:
(a) $\frac{3}{10} + 3\frac{4}{100} = 3\frac{34}{100}$
(b) $9\frac{5}{10}\frac{7}{100} + 2\frac{1}{10}\frac{3}{100} = 11\frac{70}{100}$
(c) $15\frac{6}{10}\frac{4}{100} + 14\frac{3}{10}\frac{6}{100} = 30$
(d) $7\frac{7}{100} - 4\frac{4}{100} = 3\frac{3}{100}$
(e) $8\frac{6}{100} - 5\frac{3}{100} = 3\frac{3}{100}$
(f) $12\frac{6}{10}\frac{2}{100} - \frac{9}{10}\frac{9}{100} = 11\frac{63}{100}$
Figure it Out - 3.4 (Pages 186-188)
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1. Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
4.5, 4.50, and 04.50 are the same.
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2. Identify the decimal number in the last number line in Figure (b) denoted by '?'.
4.19
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3. Make such number lines for the decimal numbers: (a) 9.876 (b) 0.407.
(a) Successive magnification number lines dividing intervals between 9 and 10 down to thousandths to locate 9.876.
(b) Successive magnification number lines dividing intervals between 0 and 1 down to thousandths to locate 0.407. -
4. a) In the number line shown below, what decimal numbers do the boxes labelled 'a', 'b', and 'c' denote?
a = 6.0, b = 7.5, c = 9.0
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b) Using similar reasoning find out the decimal numbers in the boxes below.
d = 4.4, e = 4.5, f = 4.4, g = 4.5, h = 4.9
Figure it Out - 3.5 (Page 194)
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1. Find the sums
(a) $5.3 + 2.6 = 7.9$
(b) $18 + 8.8 = 26.8$
(c) $2.15 + 5.26 = 7.41$
(d) $9.01 + 9.10 = 18.11$
(e) $29.19 + 9.91 = 39.10$
(f) $0.934 + 0.6 = 1.534$
(g) $0.75 + 0.03 = 0.78$
(h) $6.236 + 0.487 = 6.723$ -
2. Find the differences
(a) $5.6 - 2.3 = 3.3$
(b) $18 - 8.8 = 9.2$
(c) $10.4 - 4.5 = 5.9$
(d) $17 - 16.198 = 0.802$
(e) $17 - 0.05 = 16.95$
(f) $34.505 - 18.1 = 16.405$
(g) $9.9 - 9.09 = 0.81$
(h) $6.236 - 0.487 = 5.749$
Figure it Out - 3.6 (Pages 200-203)
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1. Convert the following fractions into decimals:
(a) $\frac{5}{100} = 0.05$
(b) $\frac{16}{1000} = 0.016$
(c) $\frac{12}{10} = 1.2$
(d) $\frac{254}{1000} = 0.254$ -
2. Convert the following decimals into a sum of tenths, hundredths and thousandths:
(a) $0.34 = \frac{3}{10} + \frac{4}{100}$
(b) $1.02 = 1 + \frac{0}{10} + \frac{2}{100}$
(c) $0.8 = \frac{8}{10}$
(d) $0.362 = \frac{3}{10} + \frac{6}{100} + \frac{2}{1000}$ -
3. What decimal number does each letter represent in the number line below?
a = 6.45, b = 6.56, c = 6.54
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4. Arrange the following quantities in descending order:
(a) 11.01, 1.011, 1.101, 11.10, 1.01: 11.10, 11.01, 1.101, 1.011, 1.01
(b) 2.567, 2.675, 2.768, 2.499, 2.698: 2.768, 2.698, 2.675, 2.567, 2.499
(c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g: 4.678 g, 4.666 g, 4.656 g, 4.600 g, 4.595 g
(d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m: 33.331 m, 33.313 m, 33.31 m, 33.133 m, 33.13 m -
5. Using the digits 1, 4, 0, 8, and 6 make:
(a) the decimal number closest to 30: 28.641
(b) the smallest possible decimal number between 100 and 1000: 104.68 -
6. Will a decimal number with more digits be greater than a decimal number with fewer digits?
No, for example, 0.5 is greater than 0.48 even though 0.48 has more digits.
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7. Pratap 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.
$0.25 + 0.3 + 0.5 + 0.2 + 0.05 = 1.30$ kg
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8. Rajesh 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 to the dairy in the last three days.
First 3 days total = $3.79 + 4.2 + 4.25 = 12.24$ L
Last 3 days total = $25 - 12.24 = 12.76$ L -
9. Sudhir weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
$35.75 - 34.50 = 1.25$ kg
He has lost weight by 1.25 kg. -
10. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ...
Next terms follow the alternating/operating rule to continue the sequence accurately.
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11. How many millimeters make 1 kilometer?
$1 \text{ km} = 1000 \text{ m} = 1000 \times 1000 \text{ mm} = 10,00,000 \text{ mm}$
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12. Indian Railways offers optional travel insurance for passengers who book e-tickets. It costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
$1,00,000 \times 45 \text{ paise} = 45,00,000 \text{ paise} = ₹45,000$
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13. Which is greater?
(a) $\frac{10}{1000}$ or $\frac{1}{10}$? $\frac{1}{10}$ is greater
(b) One-hundredth or 90 thousandths? 90 thousandths (0.090) is greater than one-hundredth (0.01)
(c) One-thousandth or 90 hundredths? 90 hundredths is greater -
14. Write the decimal forms of the quantities mentioned (an example is given):
(a) 87 ones, 5 tenths and 60 hundredths = 88.10
(b) 12 tens and 12 tenths = 121.2
(c) 10 tens, 10 ones, 10 tenths, and 10 hundredths = 111.10
(d) 25 tens, 25 ones, 25 tenths, and 25 hundredths = 277.75 -
16. Write the following fractions in decimal form:
(a) $\frac{1}{2} = 0.5$
(b) $\frac{3}{2} = 1.5$
(c) $\frac{1}{4} = 0.25$
(d) $\frac{3}{4} = 0.75$
(e) $\frac{1}{5} = 0.2$
(f) $\frac{4}{5} = 0.8$
