Far and Near – Class 5 Maths Chapter 5 Notes & NCERT PDF

Class 5MathematicsChapter 5NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 5 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 5: Far and Near

Introduction

We already know centimetres and metres. In this chapter we learn kilometres for long distances and millimetres for tiny lengths, and how to change from one unit to another. We meet Shikha and Sonu measuring saris at a weaving centre, the world's tallest statues, a 3-km race, India's longest train journey (the Vivek Express) and sprouting moong seeds.

Key Ideas

1. Choosing the right unit

The height of India Gate is 42 m, a handkerchief is 40 cm, a mobile phone is 13 cm. Big things are measured in metres, small things in centimetres.

2. Different units, same measure

100 cm = 1 m

So 540 cm = 5 m 40 cm, 204 cm = 2 m 4 cm, and 750 cm = 7 m 50 cm (also written 6 m 150 cm). A double number line helps convert.

3. Measuring long distances

We can measure long distances with a long tape, a measuring wheel (rodometer), a rangefinder or a laser distance meter. Walking 100 m and counting steps helps us estimate distances around school.

1,000 m = 1 km (kilo means thousand)

4. The Vivek Express

It runs 4,187 km from Dibrugarh (Assam) to Kanniyakumari (Tamil Nadu). Distances between stations are found by subtracting their distances from Dibrugarh.

5. The world of small things

One centimetre on a scale is divided into 10 equal parts.

10 mm = 1 cm

We use millimetres to measure seeds, screws, nails and the growth of a sprout.

6. Adding, subtracting, multiplying and dividing lengths

Add or subtract like units, or convert everything to the smaller unit first.

7. Other units

Height is often measured in feet and inches: 1 inch ≈ 2 cm 5 mm and 1 foot = 12 inches ≈ 30 cm.

Worked Examples

Saji's walk: 3 km 450 m + 4 km 650 m → 7 km + 1,100 m = 8 km 100 m (or 3,450 m + 4,650 m = 8,100 m).

Electric cable: 63 m − 16 m 75 cm → 6,300 cm − 1,675 cm = 4,625 cm = 46 m 25 cm left.

Shirts: 20 × 1 m 80 cm = 20 m + 1,600 cm = 20 m + 16 m = 36 m of cloth.

Road work: 12 km 600 m laid in 6 equal days → 12,600 m ÷ 6 = 2,100 m = 2 km 100 m per day.

Vivek Express: Guwahati is 556 km and Coimbatore JN is 3,675 km from Dibrugarh → distance between them = 3,119 km.

Maths Words

Length (लंबाई), Distance (दूरी)

Millimetre — mm (मिलीमीटर)

Centimetre — cm (सेंटीमीटर)

Metre — m (मीटर)

Kilometre — km (किलोमीटर)

Convert (बदलना / रूपांतरण)

Estimate (अनुमान)

Maths in Daily Life

Buying cloth (₹100 for 5 m means ₹20 per metre), measuring our height, checking step-counter apps, reading road signs in km and following train timetables all use units of length.

Common Mistakes

Writing 204 cm as 2 m 40 cm — it is 2 m 4 cm.

Adding metres to centimetres directly (e.g. 55 cm + 2 m ≠ 57).

Forgetting that 1 km is 1,000 m, not 100 m.

Starting measurement from the edge of the ruler instead of the 0 mark.

Practice Tips

Convert to the same unit before comparing, e.g. 456 cm < 5 m because 5 m = 500 cm.

Use double number lines for conversions like 25 km = 25,000 m.

Estimate using references — an electric pole, a single-storeyed house — before measuring.

💡 Key Learning Points

✓Choose suitable units (mm, cm, m, km) for different lengths
✓Use 10 mm = 1 cm, 100 cm = 1 m and 1,000 m = 1 km to convert units
✓Compare lengths by first changing them to the same unit
✓Add, subtract, multiply and divide lengths in mixed units
✓Read distance tables like the Vivek Express route and find distances between places

👨‍🏫 Teaching Tips

→Measure 100 m on the playground with a long tape and let children count their steps
→Show the tiny mm marks on a ruler and measure seeds, screws and nails
→Grow moong sprouts in class and record their length in mm for 4 days
→Draw double number lines on the board for cm ↔ m and m ↔ km
→Use the tallest statues data to make a bar picture and compare heights
→Plan a pretend 3-km race: place water stations every 500 m on a drawn track
→Let children measure their height in feet and inches as well as cm

📋 Assessment Questions

Can the child write 5,792 cm as 57 m 92 cm?
Can the child compare 6 m 5 cm and 6 m 50 cm?
Can the child add 3 km 450 m and 4 km 650 m?
Can the child find the distance between two stations from a distance table?
Can the child draw a line of 3 cm 6 mm using a scale?

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