# 📘 Chapter 3: A Peek Beyond the Point – Complete Q&A

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# # 📄 Page 47

## Q1. Which scale helped you measure the length of the screws accurately? Why?

### Answer:

A scale with smaller divisions (millimetres) helped measure accurately because it divides 1 cm into 10 equal parts, allowing precise measurement.

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## Q2. What is the meaning of 27102 \frac{7}{10}2107​ cm (the length of the first screw)?

### Answer:

$$2 \frac{7}{10} = 2 \text{ cm} + \frac{7}{10} \text{ cm}$$2107​=2 cm+107​ cm

It means:

• 2 full centimeters
• and 7 tenths of a centimeter

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## Q3. Can you explain why the unit was divided into smaller parts to measure the screws?

### Answer:

The unit is divided into smaller parts to:

• Measure small differences accurately
• Improve precision
• Get exact values instead of rough estimates

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## Q4. Measure objects like pen, sharpener, etc.

### Answer (Example):

• Pen = 14.2 cm
• Sharpener = 3.5 cm
• Eraser = 4.1 cm

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# # 📄 Page 49

## Q1. Arrange these lengths in increasing order:

(a) $\frac{9}{10}$109​
(b) $1 \frac{7}{10}$1107​
(c) $\frac{130}{10}$10130​
(d) $13 \frac{1}{10}$13101​
(e) $10 \frac{5}{10}$10105​
(f) $7 \frac{6}{10}$7106​
(g) $6 \frac{7}{10}$6107​
(h) $\frac{4}{10}$104​

### Answer:

Convert to decimals:

• 0.9, 1.7, 13, 13.1, 10.5, 7.6, 6.7, 0.4

$$0.4 < 0.9 < 1.7 < 6.7 < 7.6 < 10.5 < 13 < 13.1$$0.4<0.9<1.7<6.7<7.6<10.5<13<13.1

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## Q2. Arrange the following in increasing order:

$4 \frac{1}{10}, \frac{4}{10}, \frac{41}{10}, 41 \frac{1}{10}$4101​,104​,1041​,41101​

### Answer:

Convert:

• 4.1, 0.4, 4.1, 41.1

$$0.4 < 4.1 = 4.1 < 41.1$$0.4<4.1=4.1<41.1

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# # 📄 Page 50

## Q. Sonu’s lower arm is 27102 \frac{7}{10}2107​ units and upper arm is 36103 \frac{6}{10}3106​ units. What is total length?

### Answer:

$$2\frac{7}{10} + 3\frac{6}{10} = 5 + \frac{13}{10} = 6\frac{3}{10}$$2107​+3106​=5+1013​=6103​

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# # 📄 Page 51

## Q1. The lengths of honeybee parts are:

• Head = $2 \frac{3}{10}$2103​
• Thorax = $5 \frac{4}{10}$5104​
• Abdomen = $7 \frac{5}{10}$7105​

Find total length.

### Answer:

$$= (2+5+7) + \frac{(3+4+5)}{10} = 14 + \frac{12}{10} = 15\frac{2}{10}$$=(2+5+7)+10(3+4+5)​=14+1012​=15102​

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## Q2. The length of Shylaja’s hand is 1241012 \frac{4}{10}12104​ and palm is 67106 \frac{7}{10}6107​. Find finger length.

### Answer:

$$12\frac{4}{10} – 6\frac{7}{10} = 5\frac{7}{10}$$12104​−6107​=5107​

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# # 📄 Page 52

## Q1. Celestial Pearl Danio = 24102 \frac{4}{10}2104​ cm, Goby = 910 \frac{9}{10}109​ cm. Find difference.

### Answer:

$$2\frac{4}{10} – \frac{9}{10} = 1\frac{5}{10}$$2104​−109​=1105​

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## Q2. Identify pattern and extend:

### (a) 4, 4.3, 4.6, ___, ___, ___, ___

Answer: 4.9, 5.2, 5.5, 5.8

### (b) 8.2, 8.7, 9.2, ___

Answer: 9.7, 10.2, 10.7, 11.2

### (c) 7.6, 8.7, ___

Answer: 9.8, 10.9, 12.0, 13.1

### (d) 5.7, 5.3, ___

Answer: 4.9, 4.5, 4.1, 3.7

### (e) 13.5, 13, 12.5, ___

Answer: 12, 11.5, 11, 10.5

### (f) 11.5, 10.4, 9.3, ___

Answer: 8.2, 7.1, 6.0, 4.9

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# # 📄 Page 58 – Figure It Out

## Q1. 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

### Answers:

(a) 7.9
(b) 26.8
(c) 7.41
(d) 18.11
(e) 39.10
(f) 1.534
(g) 0.78
(h) 6.723

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## Q2. 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

### Answers:

(a) 3.3
(b) 9.2
(c) 5.9
(d) 0.802
(e) 16.95
(f) 16.405
(g) 0.81
(h) 5.749

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# # 📄 Page 79 – Final Exercise

## Q1. Convert fractions into decimals

(a) 5/100
(b) 16/1000
(c) 12/10
(d) 254/1000

### Answers:

(a) 0.05
(b) 0.016
(c) 1.2
(d) 0.254

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## Q7. Total weight of vegetables

0.25 + 0.3 + 0.5 + 0.2 + 0.05

### Answer:

$$= 1.30 \text{ kg}$$=1.30 kg

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## Q8. Milk supplied

First 3 days:$$3.79 + 4.2 + 4.25 = 12.24$$3.79+4.2+4.25=12.24

Total = 25 L

### Answer:

$$25 – 12.24 = 12.76 \text{ L}$$25−12.24=12.76 L

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## Q9. Weight change

$$35.75 – 34.50 = 1.25$$35.75−34.50=1.25

### Answer:

He lost 1.25 kg

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## Q11. How many mm in 1 km?

### Answer:

$$1\,\text{km} = 1{,}000{,}000\,\text{mm}$$1km=1,000,000mm

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## Q12. Insurance cost

45 paise × 1 lakh

### Answer:

$$= ₹45{,}000$$=₹45,000

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📘 Chapter 3: A Peek Beyond the Point – Complete Solutions

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# # 📄 Page 47

## Q1. Which scale helped you measure accurately? Why?

### Answer:

A scale with smaller divisions (millimetre markings) helps measure more accurately because:

• It divides 1 cm into 10 equal parts (tenths)
• This allows measuring very small differences in length

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## Q2. Meaning of 27102 \frac{7}{10}2107​ cm

### Answer:

$$2 \frac{7}{10} = 2 \text{ cm } + \frac{7}{10} \text{ cm}$$2107​=2 cm +107​ cm

So, it means:

• 2 full centimeters
• plus 7 parts out of 10 (i.e., 0.7 cm)

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## Q3. Why divide units into smaller parts?

### Answer:

Units are divided into smaller parts to:

• Measure more accurately
• Detect small differences
• Improve precision

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# # 📄 Page 49

## Q1. Arrange in increasing order

Given:$$\frac{9}{10},\ 1\frac{7}{10},\ \frac{130}{10},\ 13\frac{1}{10},\ 10\frac{5}{10},\ 7\frac{6}{10},\ 6\frac{7}{10},\ \frac{4}{10}$$109​, 1107​, 10130​, 13101​, 10105​, 7106​, 6107​, 104​

### Convert to decimals:

• 0.9, 1.7, 13, 13.1, 10.5, 7.6, 6.7, 0.4

### Answer:

$$0.4 < 0.9 < 1.7 < 6.7 < 7.6 < 10.5 < 13 < 13.1$$0.4<0.9<1.7<6.7<7.6<10.5<13<13.1

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## Q2. Arrange: 4 1/10, 4/10, 41/10, 41 1/10

### Convert:

• 4.1, 0.4, 4.1, 41.1

### Answer:

$$0.4 < 4.1 = 4.1 < 41.1$$0.4<4.1=4.1<41.1

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# # 📄 Page 50

## Q: Total length of Sonu’s arm

$$2\frac{7}{10} + 3\frac{6}{10}$$2107​+3106​

### Answer:

$$= 5 + \frac{13}{10} = 6\frac{3}{10}$$=5+1013​=6103​

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# # 📄 Page 51

## Q1. Total length of honeybee

$$2\frac{3}{10} + 5\frac{4}{10} + 7\frac{5}{10}$$2103​+5104​+7105​

### Answer:

$$= (2+5+7) + \frac{(3+4+5)}{10} = 14 + \frac{12}{10} = 15\frac{2}{10}$$=(2+5+7)+10(3+4+5)​=14+1012​=15102​

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## Q2. Length of middle finger

$$12\frac{4}{10} – 6\frac{7}{10}$$12104​−6107​

### Answer:

$$= 5\frac{7}{10}$$=5107​

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# # 📄 Page 52

## Q: Difference in fish lengths

$$2\frac{4}{10} – \frac{9}{10}$$2104​−109​

### Answer:

$$= 1\frac{5}{10}$$=1105​

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## Q: Patterns

### (a)

4, 4.3, 4.6 → +0.3
Answer: 4.9, 5.2, 5.5, 5.8

### (b)

8.2, 8.7, 9.2 → +0.5
Answer: 9.7, 10.2, 10.7, 11.2

### (c)

7.6 → 8.7 (+1.1)
Answer: 9.8, 10.9, 12.0, 13.1

### (d)

5.7 → 5.3 (-0.4)
Answer: 4.9, 4.5, 4.1, 3.7

### (e)

13.5 → 13 → 12.5 (-0.5)
Answer: 12, 11.5, 11, 10.5

### (f)

11.5 → 10.4 → 9.3 (-1.1)
Answer: 8.2, 7.1, 6.0, 4.9

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# # 📄 Page 55

## Q: Identify largest & smallest

### (a)

3/10 = 0.3
3/100 = 0.03
33/100 = 0.33

Answer:

• Largest = 33/100
• Smallest = 3/100

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# # 📄 Page 56

## Q: Sum

$$15\frac{3}{10}\frac{4}{100} + 2\frac{6}{10}\frac{8}{100}$$15103​1004​+2106​1008​

### Answer:

$$= 18\frac{2}{100}$$=181002​

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# # 📄 Page 57

## Q: Difference

$$25\frac{9}{10} – 6\frac{4}{10}\frac{7}{100}$$25109​−6104​1007​

### Answer:

$$= 19\frac{4}{10}\frac{3}{100}$$=19104​1003​

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## Q: Difference

$$15\frac{3}{10}\frac{4}{100} – 2\frac{6}{10}\frac{8}{100}$$15103​1004​−2106​1008​

### Answer:

$$= 12\frac{6}{10}\frac{6}{100}$$=12106​1006​

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# # 📄 Page 58 (Figure It Out)

## 1. 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

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## 2. 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

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# # 📄 Page 64–68 (Conversions)

## mm ↔ cm

70 mm = 7.0 cm
9 mm = 0.9 cm
134 mm = 13.4 cm
2036 mm = 203.6 cm

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## cm ↔ m

36 cm = 0.36 m
50 cm = 0.5 m
0.89 m = 89 cm
4 cm = 0.04 m
325 cm = 3.25 m
2.07 m = 207 cm

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## g ↔ kg

465 g = 0.465 kg
68 g = 0.068 kg
1560 g = 1.56 kg
704 g = 0.704 kg
0.56 kg = 560 g
2.5 kg = 2500 g

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## Paise ↔ Rupee

10 p = ₹0.10
5 p = ₹0.05
36 p = ₹0.36
50 p = ₹0.50
99 p = ₹0.99
250 p = ₹2.50

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# # 📄 Page 79 (Final Exercise)

## Q1. Fractions → Decimals

(a) 5/100 = 0.05
(b) 16/1000 = 0.016
(c) 12/10 = 1.2
(d) 254/1000 = 0.254

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## Q2. Decimal expansion

(a) 0.34 = 3/10 + 4/100
(b) 1.02 = 1 + 2/100
(c) 0.8 = 8/10
(d) 0.362 = 3/10 + 6/100 + 2/1000

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## Q4. Descending order

(a)
11.10 > 11.01 > 1.101 > 1.011 > 1.01

(b)
2.768 > 2.698 > 2.675 > 2.567 > 2.499

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## Q7. Total weight

$$0.25 + 0.3 + 0.5 + 0.2 + 0.05 = 1.30 \text{ kg}$$0.25+0.3+0.5+0.2+0.05=1.30 kg

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## Q8. Milk supply

First 3 days:$$3.79 + 4.2 + 4.25 = 12.24$$3.79+4.2+4.25=12.24

Total = 25 L

Last 3 days:$$25 – 12.24 = 12.76 \text{ L}$$25−12.24=12.76 L

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## Q9. Weight change

$$35.75 – 34.50 = 1.25$$35.75−34.50=1.25

Answer: Lost 1.25 kg

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## Q11. mm in 1 km

$$1\text{ km} = 1000 \times 1000 = 1,000,000 \text{ mm}$$1 km=1000×1000=1,000,000 mm

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## Q12. Insurance

$$45 \text{ paise} = 0.45$$45 paise=0.45 $$0.45 × 100000 = ₹45,000$$0.45×100000=₹45,000

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## Q13

(a) 1/10 > 10/1000
(b) 90 thousandths > 1 hundredth
(c) 90 hundredths > 1 thousandth