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Class 7 Ganita Prakash · Chapter 3
A Peek Beyond the Point

Page-wise textbook solutions (pages 46–80) · Every step · Figures · Common mistakes · Tips

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✔ Understood 0/123

🗝️ Key ideas of this chapter

1 unit = 10 tenths · 1 tenth = 10 hundredths · 1 hundredth = 10 thousandths.
The decimal point separates the whole part from the fractional part: 70.5 = 7 tens + 5 tenths; 7.05 = 7 units + 5 hundredths.
Zeros at the end after the point do not change the value: 0.2 = 0.20 = 0.200.
Compare decimals place by place from the left; the first different digit decides.
Add and subtract by lining up the decimal points and working place by place (carry / borrow 10).
Units: 1 cm = 10 mm, 1 m = 100 cm, 1 kg = 1000 g, ₹1 = 100 paise.

📖 Textbook Page 47

📖 Page 47Measure the screws

Three more screws are placed above three scales (whole cm; half cm; tenths of a cm). Write their lengths.

Scale 1: whole cm

Scale 2: half cm

Scale 3: tenths

1Scale 1 shows only whole centimetres: the screw ends after 3 → between 3 cm and 4 cm.

2Scale 2 also shows half-centimetres: the screw ends after 3 but before 3½ → more than 3 cm but less than 3½ cm.

3Scale 3 shows tenths: the screw ends at the 2nd small mark after 3 → \(3\tfrac{2}{10}\) cm.

between 3 and 4 cm

more than 3 but less than 3½ cm

3 and 2 tenths cm

✅ Answer: Between 3 and 4 cm; more than 3 but less than 3½ cm; \(3\tfrac{2}{10}\) cm.

📖 Page 47Think

Which scale helped you measure the length of the screws accurately? Why?

1The first scale tells us only the whole number of cm.

2The third scale divides each cm into 10 equal parts, so we can count the exact small parts.

✅ Answer: The third scale (marked in tenths of a cm) — it has the smallest divisions.

📖 Page 47Think

What is the meaning of \(2\tfrac{7}{10}\) cm? Why was the unit divided into smaller parts to measure the screws?

1Go from 0 to 2 cm, then 7 more parts, each part \(\tfrac{1}{10}\) cm.

2So \(2\tfrac{7}{10}\) cm = 2 cm and 7 tenths of a cm.

3Both screws looked almost the same. Whole centimetres could not show the small difference; tenths can.

✅ Answer: \(2\tfrac{7}{10}\) cm means 2 cm + \(\tfrac{7}{10}\) cm. Smaller units let us measure small differences exactly.

📖 Page 47Measure

Measure your pen, sharpener and another object with a scale and write the lengths like \(2\tfrac{7}{10}\) cm.

1Put the 0 mark at one end of the object.

2Read the whole centimetres, then count the small marks (tenths) after it.

3Example: a pen ending 4 small marks after 13 is \(13\tfrac{4}{10}\) cm; a sharpener ending 5 marks after 2 is \(2\tfrac{5}{10}\) cm.

✅ Answer: Your own measurements (for example pen ≈ \(13\tfrac{4}{10}\) cm, sharpener ≈ \(2\tfrac{5}{10}\) cm).

📖 Page 47Write the measurements

Write the lengths of the eraser, pencil and chalk shown in the picture (page 48).

1Eraser: ends 4 small marks after 2 → \(2\tfrac{4}{10}\) cm.

2Pencil: ends 5 small marks after 4 → \(4\tfrac{5}{10}\) cm.

3Chalk: ends 4 small marks after 1 → \(1\tfrac{4}{10}\) cm.

✅ Answer: Eraser \(2\tfrac{4}{10}\) cm, pencil \(4\tfrac{5}{10}\) cm, chalk \(1\tfrac{4}{10}\) cm.

📖 Textbook Page 49

📖 Page 49Two ways

Write the lengths of the pencil box, the thumb and the leaf in two ways (example: USB cable = 4 and \(\tfrac{8}{10}\) units = \(\tfrac{48}{10}\) units).

1Read each end on its own scale (the scales have different unit lengths).

2Pencil box: about \(2\tfrac{8}{10}\) units = \(\tfrac{28}{10}\) units.

3Thumb: about \(1\tfrac{3}{10}\) units = \(\tfrac{13}{10}\) units.

4Leaf: about 11 units = \(\tfrac{110}{10}\) units.

✅ Answer: Box ≈ \(2\tfrac{8}{10}\) = \(\tfrac{28}{10}\); thumb ≈ \(1\tfrac{3}{10}\) = \(\tfrac{13}{10}\); leaf ≈ 11 = \(\tfrac{110}{10}\) units.

💡 Tip: Readings from a picture may differ by one small mark — that is fine.

📖 Page 49Increasing order

Arrange in increasing order: (a) \(\tfrac{9}{10}\) (b) \(1\tfrac{7}{10}\) (c) \(\tfrac{130}{10}\) (d) \(13\tfrac{1}{10}\) (e) \(10\tfrac{5}{10}\) (f) \(7\tfrac{6}{10}\) (g) \(6\tfrac{7}{10}\) (h) \(\tfrac{4}{10}\)

1Change each to tenths: (a) 9, (b) 17, (c) 130, (d) 131, (e) 105, (f) 76, (g) 67, (h) 4 tenths.

2Order the numbers of tenths: 4 < 9 < 17 < 67 < 76 < 105 < 130 < 131.

✅ Answer: \(\tfrac{4}{10}\) < \(\tfrac{9}{10}\) < \(1\tfrac{7}{10}\) < \(6\tfrac{7}{10}\) < \(7\tfrac{6}{10}\) < \(10\tfrac{5}{10}\) < \(\tfrac{130}{10}\) < \(13\tfrac{1}{10}\)

📖 Textbook Page 50

📖 Page 50Increasing order

Arrange in increasing order: \(4\tfrac{1}{10}\), \(\tfrac{4}{10}\), \(\tfrac{41}{10}\), \(41\tfrac{1}{10}\)

1In tenths: \(4\tfrac{1}{10}\) = 41 tenths; \(\tfrac{4}{10}\) = 4 tenths; \(\tfrac{41}{10}\) = 41 tenths; \(41\tfrac{1}{10}\) = 411 tenths.

✅ Answer: \(\tfrac{4}{10}\) < \(4\tfrac{1}{10}\) = \(\tfrac{41}{10}\) < \(41\tfrac{1}{10}\)

📖 Textbook Page 51

📖 Page 51Honeybee

Head \(2\tfrac{3}{10}\), thorax \(5\tfrac{4}{10}\), abdomen \(7\tfrac{5}{10}\) units. Find the total length.

1Units: 2 + 5 + 7 = 14.

2Tenths: 3 + 4 + 5 = 12 tenths = 1 unit and 2 tenths.

3Total = 14 + 1 + \(\tfrac{2}{10}\) = \(15\tfrac{2}{10}\) units.

✅ Answer: \(15\tfrac{2}{10}\) units

📖 Page 51Shylaja’s finger

Hand \(12\tfrac{4}{10}\) units, palm \(6\tfrac{7}{10}\) units. Find the length of the middle finger.

1Finger = \(12\tfrac{4}{10}\) − \(6\tfrac{7}{10}\).

24 tenths − 7 tenths is not possible, so take 1 unit from 12: \(11\tfrac{14}{10}\).

314 tenths − 7 tenths = 7 tenths; 11 − 6 = 5.

4Check in tenths: 124 − 67 = 57 tenths = \(5\tfrac{7}{10}\).

✅ Answer: \(5\tfrac{7}{10}\) units

💡 Tip: Start subtracting from the tenths, just like starting from the ones.

📖 Textbook Page 52

📖 Page 52Fish

A Celestial Pearl Danio is \(2\tfrac{4}{10}\) cm and a Philippine Goby is \(\tfrac{9}{10}\) cm long. Find the difference.

1In tenths: 24 tenths − 9 tenths = 15 tenths.

215 tenths = \(1\tfrac{5}{10}\) cm.

✅ Answer: \(1\tfrac{5}{10}\) cm (both fish are about as long as a finger joint).

📖 Page 52Sequences (a)

Find the change and extend: 4, \(4\tfrac{3}{10}\), \(4\tfrac{6}{10}\), ___, ___, ___, ___

1Change each time: add \(\tfrac{3}{10}\).

2Next four terms: \(4\tfrac{9}{10}\), \(5\tfrac{2}{10}\), \(5\tfrac{5}{10}\), \(5\tfrac{8}{10}\)

✅ Answer: \(4\tfrac{9}{10}\), \(5\tfrac{2}{10}\), \(5\tfrac{5}{10}\), \(5\tfrac{8}{10}\)

📖 Page 52Sequences (b)

Find the change and extend: \(8\tfrac{2}{10}\), \(8\tfrac{7}{10}\), \(9\tfrac{2}{10}\), ___, ___, ___, ___

1Change each time: add \(\tfrac{5}{10}\).

2Next four terms: \(9\tfrac{7}{10}\), \(10\tfrac{2}{10}\), \(10\tfrac{7}{10}\), \(11\tfrac{2}{10}\)

✅ Answer: \(9\tfrac{7}{10}\), \(10\tfrac{2}{10}\), \(10\tfrac{7}{10}\), \(11\tfrac{2}{10}\)

📖 Page 52Sequences (c)

Find the change and extend: \(7\tfrac{6}{10}\), \(8\tfrac{7}{10}\), ___, ___, ___, ___

1Change each time: add \(1\tfrac{1}{10}\).

2Next four terms: \(9\tfrac{8}{10}\), \(10\tfrac{9}{10}\), 12, \(13\tfrac{1}{10}\)

✅ Answer: \(9\tfrac{8}{10}\), \(10\tfrac{9}{10}\), 12, \(13\tfrac{1}{10}\)

📖 Page 52Sequences (d)

Find the change and extend: \(5\tfrac{7}{10}\), \(5\tfrac{3}{10}\), ___, ___, ___, ___

1Change each time: subtract \(\tfrac{4}{10}\).

2Next four terms: \(4\tfrac{9}{10}\), \(4\tfrac{5}{10}\), \(4\tfrac{1}{10}\), \(3\tfrac{7}{10}\)

✅ Answer: \(4\tfrac{9}{10}\), \(4\tfrac{5}{10}\), \(4\tfrac{1}{10}\), \(3\tfrac{7}{10}\)

📖 Page 52Sequences (e)

Find the change and extend: \(13\tfrac{5}{10}\), 13, \(12\tfrac{5}{10}\), ___, ___, ___, ___

1Change each time: subtract \(\tfrac{5}{10}\).

2Next four terms: 12, \(11\tfrac{5}{10}\), 11, \(10\tfrac{5}{10}\)

✅ Answer: 12, \(11\tfrac{5}{10}\), 11, \(10\tfrac{5}{10}\)

📖 Page 52Sequences (f)

Find the change and extend: \(11\tfrac{5}{10}\), \(10\tfrac{4}{10}\), \(9\tfrac{3}{10}\), ___, ___, ___, ___

1Change each time: subtract \(1\tfrac{1}{10}\).

2Next four terms: \(8\tfrac{2}{10}\), \(7\tfrac{1}{10}\), 6, \(4\tfrac{9}{10}\)

✅ Answer: \(8\tfrac{2}{10}\), \(7\tfrac{1}{10}\), 6, \(4\tfrac{9}{10}\)

📖 Textbook Page 53

📖 Page 53Hundredths

A sheet \(8\tfrac{9}{10}\) units long is folded in half. What is its length now?

1Half of 8 = 4. Half of 9 tenths = 4½ tenths.

2Split each tenth into 10 hundredths: 4½ tenths = 4 tenths + 5 hundredths.

3Length = \(4\tfrac{4}{10}\tfrac{5}{100}\) units = 4.45 units.

✅ Answer: \(4\tfrac{4}{10}\tfrac{5}{100}\) units

📖 Page 53Math Talk

How many one-hundredths make one-tenth? Can we say the length is 4 units and 45 one-hundredths?

1\(\tfrac{1}{10}\) = \(\tfrac{10}{100}\), so 10 hundredths make 1 tenth.

24 tenths = 40 hundredths; 40 + 5 = 45 hundredths.

✅ Answer: 10 hundredths = 1 tenth. Yes: \(4\tfrac{45}{100}\) units.

📖 Textbook Page 54

📖 Page 54Fill the boxes

On the scale from 0 to 2½ marked in hundredths, fill the empty boxes (lengths measured from 0).

1Each small mark is \(\tfrac{1}{100}\); each big mark is \(\tfrac{1}{10}\).

2Count big marks and then small marks for each box (reading from the picture):

3Box 1: 5 tenths + 5 hundredths = \(\tfrac{55}{100}\).

4Box 2: \(1\tfrac{55}{100}\) = \(\tfrac{155}{100}\).

5Box 3: \(1\tfrac{74}{100}\) = \(\tfrac{174}{100}\).

6Box 4: \(2\tfrac{2}{100}\) = \(\tfrac{202}{100}\).

7Box 5: \(2\tfrac{4}{10}\) = \(\tfrac{240}{100}\).

✅ Answer: \(\tfrac{55}{100}\), \(\tfrac{155}{100}\), \(\tfrac{174}{100}\), \(\tfrac{202}{100}\), \(\tfrac{240}{100}\)

📖 Page 54Same length

Explain why \(1\tfrac{1}{10}\tfrac{4}{100}\), \(1\tfrac{14}{100}\) and \(\tfrac{114}{100}\) are the same length.

1\(\tfrac{1}{10}\) = \(\tfrac{10}{100}\), so \(\tfrac{1}{10}\) + \(\tfrac{4}{100}\) = \(\tfrac{14}{100}\).

21 unit = \(\tfrac{100}{100}\), so \(1\tfrac{14}{100}\) = \(\tfrac{114}{100}\).

✅ Answer: All three equal 1.14 units.

📖 Page 54Read the wires

Write the measurements of the four wires and read them in words.

1Read where each wire ends: whole number, then tenths, then the small hundredth marks.

2Wire 1: \(5\tfrac{37}{100}\) — five and thirty-seven hundredths

3Wire 2: \(15\tfrac{3}{100}\) — fifteen and three hundredths

4Wire 3: \(7\tfrac{52}{100}\) — seven and fifty-two hundredths

5Wire 4: \(9\tfrac{80}{100}\) — nine and eighty hundredths (= nine and eight tenths)

✅ Answer: \(5\tfrac{37}{100}\), \(15\tfrac{3}{100}\), \(7\tfrac{52}{100}\), \(9\tfrac{80}{100}\)

📖 Textbook Page 55

📖 Page 55Longest & shortest (a)

Find the longest and the shortest: \(\tfrac{3}{10}\), \(\tfrac{3}{100}\), \(\tfrac{33}{100}\)

1Write each in hundredths: \(\tfrac{3}{10}\) = 30 hundredths, \(\tfrac{3}{100}\) = 3 hundredths, \(\tfrac{33}{100}\) = 33 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(\tfrac{33}{100}\), shortest \(\tfrac{3}{100}\)

📖 Page 55Longest & shortest (b)

Find the longest and the shortest: \(3\tfrac{1}{10}\), \(\tfrac{30}{10}\), \(1\tfrac{3}{10}\)

1Write each in hundredths: \(3\tfrac{1}{10}\) = 310 hundredths, \(\tfrac{30}{10}\) = 300 hundredths, \(1\tfrac{3}{10}\) = 130 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(3\tfrac{1}{10}\), shortest \(1\tfrac{3}{10}\)

📖 Page 55Longest & shortest (c)

Find the longest and the shortest: \(\tfrac{45}{100}\), \(\tfrac{54}{100}\), \(\tfrac{5}{10}\), \(\tfrac{4}{10}\)

1Write each in hundredths: \(\tfrac{45}{100}\) = 45 hundredths, \(\tfrac{54}{100}\) = 54 hundredths, \(\tfrac{5}{10}\) = 50 hundredths, \(\tfrac{4}{10}\) = 40 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(\tfrac{54}{100}\), shortest \(\tfrac{4}{10}\)

📖 Page 55Longest & shortest (d)

Find the longest and the shortest: \(3\tfrac{6}{10}\), \(3\tfrac{6}{100}\), \(3\tfrac{6}{10}\tfrac{6}{100}\)

1Write each in hundredths: \(3\tfrac{6}{10}\) = 360 hundredths, \(3\tfrac{6}{100}\) = 306 hundredths, \(3\tfrac{6}{10}\tfrac{6}{100}\) = 366 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(3\tfrac{6}{10}\tfrac{6}{100}\), shortest \(3\tfrac{6}{100}\)

📖 Textbook Page 56

📖 Page 56Longest & shortest (e)

Find the longest and the shortest: \(\tfrac{8}{10}\tfrac{2}{100}\), \(\tfrac{9}{100}\), \(1\tfrac{8}{100}\)

1Write each in hundredths: \(\tfrac{8}{10}\tfrac{2}{100}\) = 82 hundredths, \(\tfrac{9}{100}\) = 9 hundredths, \(1\tfrac{8}{100}\) = 108 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(1\tfrac{8}{100}\), shortest \(\tfrac{9}{100}\)

📖 Page 56Longest & shortest (f)

Find the longest and the shortest: \(7\tfrac{3}{10}\tfrac{5}{100}\), \(7\tfrac{5}{10}\), \(7\tfrac{41}{100}\)

1Write each in hundredths: \(7\tfrac{3}{10}\tfrac{5}{100}\) = 735 hundredths, \(7\tfrac{5}{10}\) = 750 hundredths, \(7\tfrac{41}{100}\) = 741 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(7\tfrac{5}{10}\), shortest \(7\tfrac{3}{10}\tfrac{5}{100}\)

📖 Page 56Longest & shortest (g)

Find the longest and the shortest: \(\tfrac{65}{10}\tfrac{15}{100}\), \(5\tfrac{87}{100}\), \(5\tfrac{7}{100}\)

1Write each in hundredths: \(\tfrac{65}{10}\tfrac{15}{100}\) = 665 hundredths, \(5\tfrac{87}{100}\) = 587 hundredths, \(5\tfrac{7}{100}\) = 507 hundredths

2Compare the numbers of hundredths.

✅ Answer: Longest \(\tfrac{65}{10}\tfrac{15}{100}\), shortest \(5\tfrac{7}{100}\)

📖 Textbook Page 57

📖 Page 57Math Talk

Are the two methods for \(15\tfrac{3}{10}\tfrac{4}{100}\) + \(2\tfrac{6}{10}\tfrac{8}{100}\) different? How are they like 483 + 268?

1Both methods add units with units, tenths with tenths and hundredths with hundredths.

212 hundredths = 1 tenth + 2 hundredths (carry), 10 tenths = 1 unit (carry).

3In 483 + 268 we also add place by place and carry: 11 ones = 1 ten + 1 one, 15 tens = 1 hundred + 5 tens.

✅ Answer: No — both add place by place and carry 10 of a place to the next bigger place, exactly as in 483 + 268. Answer: \(18\tfrac{2}{100}\).

📖 Textbook Page 58

📖 Page 58Math Talk

Find \(25\tfrac{9}{10}\) − \(6\tfrac{4}{10}\tfrac{7}{100}\) by converting to hundredths.

1\(25\tfrac{9}{10}\) = \(\tfrac{2590}{100}\); \(6\tfrac{4}{10}\tfrac{7}{100}\) = \(\tfrac{647}{100}\).

22590 − 647 = 1943

3\(\tfrac{1943}{100}\) = \(19\tfrac{43}{100}\).

✅ Answer: \(19\tfrac{4}{10}\tfrac{3}{100}\) = 19.43

📖 Page 58Math Talk

How is \(15\tfrac{3}{10}\tfrac{4}{100}\) − \(2\tfrac{6}{10}\tfrac{8}{100}\) like 653 − 268?

1When a place is too small we borrow 1 from the next bigger place (1 tenth = 10 hundredths, 1 unit = 10 tenths).

2Same as borrowing 1 ten = 10 ones in 653 − 268 = 385.

✅ Answer: Same borrowing idea. Answer: \(12\tfrac{6}{10}\tfrac{6}{100}\) = 12.66

📖 Page 58Figure it Out (a)

Find: \(\tfrac{3}{10}\) + \(3\tfrac{4}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 334 hundredths = 3 and 34 hundredths.

✅ Answer: \(3\tfrac{34}{100}\) = 3.34

📖 Page 58Figure it Out (b)

Find: \(9\tfrac{5}{10}\tfrac{7}{100}\) + \(2\tfrac{1}{10}\tfrac{3}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 1170 hundredths = 11 and 70 hundredths.

✅ Answer: \(11\tfrac{70}{100}\) = 11.70

📖 Page 58Figure it Out (c)

Find: \(15\tfrac{6}{10}\tfrac{4}{100}\) + \(14\tfrac{3}{10}\tfrac{6}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 3000 hundredths = 30 and 0 hundredths.

✅ Answer: 30 = 30.00

📖 Page 58Figure it Out (d)

Find: \(7\tfrac{7}{100}\) − \(4\tfrac{4}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 303 hundredths = 3 and 3 hundredths.

✅ Answer: \(3\tfrac{3}{100}\) = 3.03

📖 Page 58Figure it Out (e)

Find: \(8\tfrac{6}{100}\) − \(5\tfrac{3}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 303 hundredths = 3 and 3 hundredths.

✅ Answer: \(3\tfrac{3}{100}\) = 3.03

📖 Page 58Figure it Out (f)

Find: \(12\tfrac{6}{10}\tfrac{2}{100}\) − \(\tfrac{9}{10}\tfrac{9}{100}\)

1Change both to hundredths, then add or subtract.

2Result = 1163 hundredths = 11 and 63 hundredths.

✅ Answer: \(11\tfrac{63}{100}\) = 11.63

📖 Textbook Page 61

📖 Page 61How big?

(a) How many thousandths make one unit? (b) …one tenth? (c) …one hundredth? (d) How many tenths make one ten? (e) How many hundredths make one ten?

1(a) 1 = \(\tfrac{1000}{1000}\) → 1000

2(b) \(\tfrac{1}{10}\) = \(\tfrac{100}{1000}\) → 100

3(c) \(\tfrac{1}{100}\) = \(\tfrac{10}{1000}\) → 10

4(d) 10 = \(\tfrac{100}{10}\) → 100

5(e) 10 = \(\tfrac{1000}{100}\) → 1000

✅ Answer: (a) 1000 (b) 100 (c) 10 (d) 100 (e) 1000

📖 Page 61Math Talk

Can \(4\tfrac{2}{10}\) be written as 42? How would we know if 42 means 4 tens and 2 units or 4 units and 2 tenths?

142 already means 4 tens and 2 units.

2We need a mark to show where the whole number ends — the decimal point.

3\(4\tfrac{2}{10}\) = 4.2 and 42 = 42.

✅ Answer: No. We write 4.2 — the decimal point separates units from tenths.

📖 Textbook Page 63

📖 Page 63Place value table

Write each quantity in decimal form and read it: (a)–(h) as listed in the textbook.

1Put each digit in its place: hundreds, tens, units . tenths, hundredths, thousandths.

2Write 0 in any empty place between digits.

3(a) 2 ones, 3 tenths and 5 hundredths → 2.35 (two point three five)

4(b) 1 ten and 5 tenths → 10.5 (ten point five)

5(c) 4 ones and 6 hundredths → 4.06 (four point zero six)

6(d) 1 hundred, 1 one and 1 hundredth → 101.01 (one hundred one point zero one)

7(e) \(\tfrac{8}{100}\) and \(\tfrac{9}{10}\) → 0.98 (zero point nine eight)

8(f) \(\tfrac{5}{100}\) → 0.05 (zero point zero five)

9(g) \(\tfrac{1}{10}\) → 0.1 (zero point one)

10(h) \(2\tfrac{1}{100}\), \(4\tfrac{1}{10}\) and \(7\tfrac{7}{1000}\) → 2.01, 4.1, 7.007 (two point zero one; four point one; seven point zero zero seven)

Decimal	Hundreds	Tens	Units	Tenths	Hundredths	Thousandths
2.35			2	3	5
10.5		1	0	5
4.06			4	0	6
101.01	1	0	1	0	1
0.98			0	9	8
0.05			0	0	5
0.1			0	1
2.01			2	0	1
4.1			4	1
7.007			7	0	0	7

✅ Answer: (a) 2.35; (b) 10.5; (c) 4.06; (d) 101.01; (e) 0.98; (f) 0.05; (g) 0.1; (h) 2.01, 4.1, 7.007

📖 Textbook Page 64

📖 Page 64Decimal form

Write in decimal form: (a) 234 hundredths (b) 105 tenths.

1(a) 234 hundredths = 200 + 30 + 4 hundredths = 2 + 3 tenths + 4 hundredths = 2.34

2(b) 105 tenths = 100 + 5 tenths = 10 + 5 tenths = 10.5

✅ Answer: (a) 2.34 (b) 10.5

📖 Textbook Page 65

📖 Page 65mm ↔ cm

Fill in: 70 mm = __; __ = 0.9 cm; 134 mm = __; __ = 203.6 cm

110 mm = 1 cm, so divide mm by 10 (or multiply cm by 10).

270 mm = 7 cm (= 7.0 cm)

30.9 cm = 9 mm

4134 mm = 13.4 cm

5203.6 cm = 2036 mm

✅ Answer: 7 cm; 9 mm; 13.4 cm; 2036 mm

📖 Textbook Page 66

📖 Page 66cm ↔ m

Fill in: 36 cm = __; 50 cm = __; __ = 0.89 m; 4 cm = __; 325 cm = __; __ = 2.07 m

1100 cm = 1 m, so divide cm by 100.

236 cm = 0.36 m; 50 cm = 0.5 m; 0.89 m = 89 cm

34 cm = 0.04 m; 325 cm = 3.25 m; 2.07 m = 207 cm

✅ Answer: 0.36 m; 0.5 m; 89 cm; 0.04 m; 3.25 m; 207 cm

⚠️ Common mistake: Writing 4 cm = 0.4 m. 4 cm is 4 hundredths of a metre: 0.04 m.

📖 Page 66Think

How many mm does 1 metre have? Can we write 1 mm = \(\tfrac{1}{1000}\) m?

11 m = 100 cm and 1 cm = 10 mm → 1 m = 100 × 10 = 1000 mm.

2So 1 mm is one-thousandth of a metre.

✅ Answer: 1000 mm; yes, 1 mm = \(\tfrac{1}{1000}\) m = 0.001 m.

📖 Textbook Page 67

📖 Page 67g ↔ kg

Fill in: 465 g = __; 68 g = __; 1560 g = __; 704 g = __; __ = 0.56 kg; __ = 2.5 kg

11000 g = 1 kg, so divide grams by 1000 (3 places).

2465 g = 0.465 kg; 68 g = 0.068 kg; 1560 g = 1.56 kg

3704 g = 0.704 kg; 0.56 kg = 560 g; 2.5 kg = 2500 g

✅ Answer: 0.465 kg; 0.068 kg; 1.56 kg; 0.704 kg; 560 g; 2500 g

⚠️ Common mistake: Writing 68 g = 0.68 kg. 68 g = 68 thousandths of a kg = 0.068 kg.

📖 Textbook Page 69

📖 Page 69paise ↔ rupee

Fill in: 10 p = __; __ p = ₹0.05; __ p = ₹0.36; __ = ₹0.50; 99 p = __; 250 p = __

1100 paise = ₹1, so divide paise by 100.

210 p = ₹0.10; ₹0.05 = 5 p; ₹0.36 = 36 p

3₹0.50 = 50 p; 99 p = ₹0.99; 250 p = ₹2.50

✅ Answer: ₹0.10; 5 p; 36 p; 50 p; ₹0.99; ₹2.50

📖 Textbook Page 70

📖 Page 70Number line

Name all the divisions between 1 and 1.1 on the number line.

1The part from 1 to 1.1 is split into 10 equal parts, each \(\tfrac{1}{100}\) = 0.01.

✅ Answer: 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09

📖 Page 70Number line

Identify the decimal numbers at A, B, C and D (the line from 5 to 5.4 has hundredth marks).

1Each small mark is 0.01.

2A is 1 mark before 5.1 → 5.09

3B is 3 marks after 5.1 → 5.13

4C is at 5.2 (10 marks after 5.1)

5D is 1 mark after 5.3 → 5.31

✅ Answer: A = 5.09, B = 5.13, C = 5.2, D = 5.31

📖 Textbook Page 71

📖 Page 71Zero dilemma

0.2, 0.20, 0.200, 0.02, 0.002: which is the smallest and which is the largest? Which of 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50 are the same?

1Zeros at the END after the point (or at the very start) do not change the value: 0.2 = 0.20 = 0.200.

20.02 has 2 hundredths and 0.002 has 2 thousandths.

34.5 = 4.50 = 04.50 (4 and 5 tenths).

44.05 = 4.050 (4 and 5 hundredths).

54.005 and 0.405 are different from all others.

✅ Answer: Largest 0.2 (= 0.20 = 0.200), smallest 0.002. Same: 4.5 = 4.50 = 04.50 and 4.05 = 4.050.

📖 Page 71Zoom in

Figure (b) zooms in level by level like Figure (a). What number does ‘?’ show?

Each level zooms into the marked part of the line above it.

1Level 1 (0 to 10): the arrow is at 3.

2Level 2 (3 to 4): the arrow is between 3.0 and 3.1.

3Level 3 (3.0 to 3.1): the arrow is between 3.05 and 3.06.

4Level 4 (3.05 to 3.06): the ‘?’ is at the 9th mark → 3.059.

Each level zooms into the marked part of the line above it.

✅ Answer: 3.059

📖 Page 71Make number lines

Make zoom-in number lines for (a) 9.876 (b) 0.407.

1(a) 0–10: mark 9 → 9 to 10: mark 9.8 → 9.8 to 9.9: mark 9.87 → 9.87 to 9.88: mark 9.876.

2(b) 0–1: mark 0.4 → 0.4 to 0.5: mark 0.40 → 0.40 to 0.41: mark 0.407.

✅ Answer: Zoom in one place value at a time, as shown in the steps.

📖 Page 71Boxes a, b, c

The line from 5 to 10 has 10 equal divisions. b is 7.5. Find a and c.

15 units ÷ 10 divisions = \(\tfrac{1}{2}\) unit per division.

2a is 2 divisions after 5 → 5 + 1 = 6.

3b is 5 divisions → 7.5 ✔

4c is 9 divisions → 5 + 4.5 = 9.5.

✅ Answer: a = 6, c = 9.5

📖 Textbook Page 72

📖 Page 72Boxes d–h

Find the numbers in boxes d, e (line 8 to 8.1 with 10 divisions) and f, g, h (line 4.3 to 4.8 with 10 divisions).

18 to 8.1: 0.1 ÷ 10 = 0.01 per division → d = 8.01, e = 8.05.

24.3 to 4.8: 0.5 ÷ 10 = 0.05 per division → f = 4.35, g = 4.5, h is 1 division after 4.8 = 4.85.

✅ Answer: d = 8.01, e = 8.05, f = 4.35, g = 4.5, h = 4.85

📖 Textbook Page 73

📖 Page 73Math Talk

When comparing decimals digit by digit, why can we stop at the first place where the digits differ?

1Say 6.456 and 6.465 first differ at hundredths (5 and 6).

26.465 has at least 1 hundredth (= 10 thousandths) more there.

3All the digits after it together are always LESS than 1 hundredth (at most 0.0099…).

4So later digits can never make up the difference.

✅ Answer: Because one unit of that place is worth more than all the smaller places put together.

📖 Page 73Which is greater (a)

Which is greater: 1.23 or 1.32?

1Compare place by place from the left (units first).

✅ Answer: 1.32

📖 Page 73Which is greater (b)

Which is greater: 3.81 or 13.800?

1Compare place by place from the left (units first).

✅ Answer: 13.800

📖 Page 73Which is greater (c)

Which is greater: 1.009 or 1.090?

1Compare place by place from the left (units first).

✅ Answer: 1.090

📖 Page 73Closest decimals

Of 0.9, 1.1, 1.01, 1.11 which is closest to 1.09? Which of 3.56, 3.65, 3.099 is closest to 4? Which of 0.8, 0.69, 1.08 is closest to 1?

11.09: distances 0.19, 0.01, 0.08, 0.02 → 1.1.

24: distances 0.44, 0.35, 0.901 → 3.65.

31: distances 0.2, 0.31, 0.08 → 1.08.

✅ Answer: 1.1; 3.65; 1.08

📖 Page 73Math Talk

Use the digits 4, 1, 8, 2 and 5 to make numbers as close as possible to 25 in the patterns ▢▢.▢▢▢, ▢.▢▢▢ and ▢▢▢.▢▢.

1▢▢.▢▢▢: whole part 25, then the smallest decimal part from 1, 4, 8 → 25.148 (only 0.148 away). 24.851 is 0.149 away — a little farther.

2▢.▢▢▢ (4 digits): as big as possible → 8.542.

3▢▢▢.▢▢: as small as possible → 124.58.

✅ Answer: 25.148; 8.542; 124.58

📖 Textbook Page 74

📖 Page 74Cloth

Priya needs 2.7 m and Shylaja 3.5 m of cloth. Find the total and the difference.

12.7 + 3.5: 7 + 5 = 12 tenths = 1.2 → 6.2 m.

23.5 − 2.7: take 1 unit → 2 + 15 tenths; 15 − 7 = 8 tenths → 0.8 m.

✅ Answer: Total 6.2 m; Shylaja’s is 0.8 m longer.

📖 Textbook Page 75

📖 Page 75Try This

Write the place value computation for 84.691 − 77.345 and its compact form.

1Thousandths: 1 − 5 not possible → borrow: 11 − 5 = 6.

2Hundredths: (9 − 1) − 4 = 4.

3Tenths: 6 − 3 = 3.

4Units: 4 − 7 not possible → borrow 1 ten: 14 − 7 = 7.

5Tens: (8 − 1) − 7 = 0.

✅ Answer: 84.691 − 77.345 = 7.346

📖 Page 75Figure it Out · Q1(a)

Find the sum: 5.3 + 2.6