Far and Near

We convert all measurements to the same unit (cm) before comparing.

(a) 456 cm ___ 5 m

Convert 5 m to cm: $5 \text{ m} = 5 \times 100 = 500 \text{ cm}$

Compare: $456 \text{ cm}$ vs $500 \text{ cm}$

$$456 < 500$$

$$\boxed{456 \text{ cm} < 5 \text{ m}}$$

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(b) 55 cm + 200 cm ___ 200 cm + 54 cm

Left side: $55 + 200 = 255 \text{ cm}$

Right side: $200 + 54 = 254 \text{ cm}$

Compare: $255$ vs $254$

$$\boxed{55 \text{ cm} + 200 \text{ cm} > 200 \text{ cm} + 54 \text{ cm}}$$

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(c) 6 m 5 cm ___ 6 m 50 cm

Convert both to cm:
- $6 \text{ m } 5 \text{ cm} = 600 + 5 = 605 \text{ cm}$
- $6 \text{ m } 50 \text{ cm} = 600 + 50 = 650 \text{ cm}$

Compare: $605$ vs $650$

$$\boxed{6 \text{ m } 5 \text{ cm} < 6 \text{ m } 50 \text{ cm}}$$

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(d) 2 m 150 cm ___ 3 m 50 cm

Convert both to cm:
- $2 \text{ m } 150 \text{ cm} = 200 + 150 = 350 \text{ cm}$
- $3 \text{ m } 50 \text{ cm} = 300 + 50 = 350 \text{ cm}$

Compare: $350$ vs $350$

$$\boxed{2 \text{ m } 150 \text{ cm} = 3 \text{ m } 50 \text{ cm}}$$

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(e) 238 cm ___ 138 cm + 1 m

Right side: $138 \text{ cm} + 1 \text{ m} = 138 + 100 = 238 \text{ cm}$

Compare: $238$ vs $238$

$$\boxed{238 \text{ cm} = 138 \text{ cm} + 1 \text{ m}}$$

Note: This question refers to a figure/table of statue heights that is not fully visible in the OCR. The standard data used in NCERT Class 5 for this question is:
- Statue of Unity (India): 182 m
- Spring Temple Buddha (China): 128 m
- Statue of Liberty (USA): 93 m
- Christ the Redeemer (Brazil): 38 m
- Motherland Calls (Russia): 85 m

The tallest statue in the world (as per the textbook context) is the Statue of Unity at 182 m.

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(a) Difference between the tallest statue (Statue of Unity) and the Statue of Liberty:

$$182 \text{ m} - 93 \text{ m} = 89 \text{ m}$$

The difference is 89 m.

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(b) Statues whose heights have the least difference:

Compare all pairs:
- Motherland Calls (85 m) and Statue of Liberty (93 m): $93 - 85 = 8$ m
- Spring Temple Buddha (128 m) and Statue of Unity (182 m): $182 - 128 = 54$ m

The least difference is between the Motherland Calls and the Statue of Liberty (difference = 8 m).

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(c) Statues whose heights have the largest difference:

The largest difference is between the tallest and the shortest statues:
- Statue of Unity (182 m) and Christ the Redeemer (38 m): $182 - 38 = 144$ m

The largest difference is between the Statue of Unity and Christ the Redeemer (difference = 144 m).

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(d) Height of which statue doubled equals the Statue of Unity (182 m)?

We need: $2 \times h = 182$

$$h = 182 \div 2 = 91 \text{ m}$$

The statue closest to 91 m is the Statue of Liberty (93 m). Based on the textbook data, the answer is the Statue of Liberty (approximately, depending on exact figures given in the figure).

Given: $1 \text{ km} = 1{,}000 \text{ m}$

Number of ropes needed $= 1{,}000 \div \text{length of each rope}$

| Length of rope | Calculation | Number of ropes needed |
|---|---|---|
| 1,000 m | $1{,}000 \div 1{,}000$ | 1 |
| 100 m | $1{,}000 \div 100$ | 10 |
| 10 m | $1{,}000 \div 10$ | 100 |
| 200 m | $1{,}000 \div 200$ | 5 |
| 500 m | $1{,}000 \div 500$ | 2 |
| 250 m | $1{,}000 \div 250$ | 4 |

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Water stations are placed every $500 \text{ m}$.

Number of water stations $= 3{,}000 \div 500 = 6$

However, a water station at the finish line (3,000 m) may not be needed as a separate station. Based on standard interpretation, stations are placed after the start and before or at the finish:

Positions from the starting point:
$$500 \text{ m},\ 1{,}000 \text{ m},\ 1{,}500 \text{ m},\ 2{,}000 \text{ m},\ 2{,}500 \text{ m},\ 3{,}000 \text{ m}$$

Number of water stations = 6

They will be placed at: 500 m, 1,000 m, 1,500 m, 2,000 m, 2,500 m, and 3,000 m from the starting point.

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Children stand at every $300 \text{ m}$.

Number of positions $= 3{,}000 \div 300 = 10$

Positions from the starting point:
$$300 \text{ m},\ 600 \text{ m},\ 900 \text{ m},\ 1{,}200 \text{ m},\ 1{,}500 \text{ m},\ 1{,}800 \text{ m},\ 2{,}100 \text{ m},\ 2{,}400 \text{ m},\ 2{,}700 \text{ m},\ 3{,}000 \text{ m}$$

Number of children needed = 10

They will stand at: 300 m, 600 m, 900 m, 1,200 m, 1,500 m, 1,800 m, 2,100 m, 2,400 m, 2,700 m, and 3,000 m from the starting point.

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Flags are placed every $50 \text{ m}$.

Total number of flag positions (not counting the start) $= 3{,}000 \div 50 = 60$

Flags are placed alternately (Red, Blue, Red, Blue, …) starting from the first position at 50 m.

Total flags = 60

Since flags alternate:
- Red flags = $60 \div 2 = 30$
- Blue flags = $60 \div 2 = 30$

30 red flags and 30 blue flags are needed till the finish line.

Note: The specific sub-questions for this table are not fully visible in the OCR. Below are the key facts that can be derived from the table, which are typically asked:

Total distance of the journey (Dibrugarh to Kanniyakumari):
$$= 4{,}187 \text{ km}$$

Distance between consecutive stations (for reference):
- Dibrugarh to Dimapur: $306 \text{ km}$
- Dimapur to Guwahati: $556 - 306 = 250 \text{ km}$
- Guwahati to Jalpaiguri Road: $983 - 556 = 427 \text{ km}$
- Jalpaiguri Road to Bhubaneswar: $2{,}007 - 983 = 1{,}024 \text{ km}$
- Bhubaneswar to Visakhapatnam: $2{,}450 - 2{,}007 = 443 \text{ km}$
- Visakhapatnam to Vijayawada JN: $2{,}800 - 2{,}450 = 350 \text{ km}$
- Vijayawada JN to Coimbatore JN: $3{,}675 - 2{,}800 = 875 \text{ km}$
- Coimbatore JN to Kanniyakumari: $4{,}187 - 3{,}675 = 512 \text{ km}$

Students should use the table to answer specific questions about distances between stations as directed by the teacher.

Concept used: $10 \text{ mm} = 1 \text{ cm}$

Convert each length to mm for ease of measurement:

1. $5 \text{ cm } 5 \text{ mm} = 50 + 5 = 55 \text{ mm}$
2. $3 \text{ cm } 6 \text{ mm} = 30 + 6 = 36 \text{ mm}$
3. $8 \text{ cm } 3 \text{ mm} = 80 + 3 = 83 \text{ mm}$
4. $36 \text{ mm} = 3 \text{ cm } 6 \text{ mm}$
5. $67 \text{ mm} = 6 \text{ cm } 7 \text{ mm}$

Steps to draw each line:
- Place the scale on the notebook.
- Mark the starting point at 0.
- Mark the ending point at the required length.
- Join the two points with a sharp pencil to draw the line.

How to draw 36 mm and 67 mm lines:

For 36 mm: Since most scales show both cm and mm markings, place the scale and mark from 0 to the 36 mm mark (which is the same as 3 cm 6 mm mark). Draw the line.

For 67 mm: Mark from 0 to the 67 mm mark (which is the same as 6 cm 7 mm). Draw the line.

*Alternatively*, if the scale only shows cm, convert: $36 \text{ mm} = 3.6 \text{ cm}$ and $67 \text{ mm} = 6.7 \text{ cm}$, and mark accordingly between the cm markings.

Relationships used:
$$10 \text{ mm} = 1 \text{ cm}, \quad 100 \text{ cm} = 1 \text{ m}, \quad 1{,}000 \text{ m} = 1 \text{ km}$$

mm ↔ cm number line:
For every 1 cm, there are 10 mm.
- 1 cm = 10 mm
- 2 cm = 20 mm
- 5 cm = 50 mm
- 10 cm = 100 mm

cm ↔ m number line:
For every 1 m, there are 100 cm.
- 1 m = 100 cm
- 2 m = 200 cm
- 5 m = 500 cm
- 10 m = 1,000 cm

m ↔ km number line:
For every 1 km, there are 1,000 m.
- 1 km = 1,000 m
- 2 km = 2,000 m
- 5 km = 5,000 m

*(Students should fill in the blanks on the number lines in their textbook using the above relationships.)*