Far and Near
Millimetres, centimetres, metres, and kilometres: converting between them, and adding, subtracting, multiplying, and dividing lengths.
- Choosing the right unit: mm, cm, m, or km
- Converting between units (1 cm = 10 mm, 1 m = 100 cm, 1 km = 1,000 m)
- Comparing lengths written in different units
- Adding, subtracting, multiplying, and dividing lengths
- Estimating heights, and inches and feet
🏏 Let’s Begin: How Long Is It?
Before a cricket match in the gali, Arjun measured the pitch with his feet. “22 steps!” he said. His friend Zoya measured with her feet: “26 steps!”
Who is right? Both! Their feet are different sizes. That’s why we use standard units like metres. Everyone’s metre is the same.
📏 Part 1: The Family of Length Units
| Unit | How big? | Use it for |
|---|---|---|
| Millimetre (mm) | Thickness of a 1-rupee coin, about 1 mm | Ant, seed, sprout, screw |
| Centimetre (cm) | Width of your little finger, about 1 cm | Pencil, book, mobile phone |
| Metre (m) | One big step of an adult, about 1 m | Room, saree, height of a building |
| Kilometre (km) | About 12–15 minutes of walking | Distance between towns |
Kilo means thousand, centi means hundredth, and milli means thousandth.
🔁 Part 2: Converting Units
Bigger unit → smaller unit: multiply
- 7 cm = 7 × 10 = 70 mm
- 3 m 45 cm = 300 cm + 45 cm = 345 cm
- 5 km 80 m = 5,000 m + 80 m = 5,080 m (don’t write 5,800!)
Smaller unit → bigger unit: split it up
- 73 mm = 70 mm + 3 mm = 7 cm 3 mm
- 628 cm = 600 cm + 28 cm = 6 m 28 cm
- 12,305 m = 12,000 m + 305 m = 12 km 305 m
7 km 60 m = 7,060 m, not 760 m ❌
✅ cm needs 2 places after metres, and m needs 3 places after km.
Comparing lengths
Which is longer, 3 m 8 cm or 350 cm? First, make them the same unit: 3 m 8 cm = 308 cm. Now it’s easy: 308 cm < 350 cm. So 350 cm is longer.
🧮 Part 3: Adding and Subtracting Lengths
Adding: Pooja cycled 2 km 750 m to school and 1 km 600 m to tuition. How far in total?
km: 2 + 1 = 3 km · m: 750 + 600 = 1,350 m = 1 km 350 m
Total = 3 km + 1 km 350 m = 4 km 350 m
Or convert everything to metres: 2,750 + 1,600 = 4,350 m = 4 km 350 m ✅
Subtracting: A tailor had 10 m of cloth. He used 3 m 65 cm. How much is left?
10 m = 1,000 cm, and 3 m 65 cm = 365 cm. So 1,000 − 365 = 635 cm = 6 m 35 cm.
✖️ Part 4: Multiplying and Dividing Lengths
Multiply: One kurta needs 2 m 40 cm of cloth. How much do 5 kurtas need?
5 × 2 m = 10 m, and 5 × 40 cm = 200 cm = 2 m. Total = 12 m.
Divide: A 9 km 600 m canal is cleaned equally in 4 days. How much is cleaned each day?
9 km 600 m = 9,600 m. So 9,600 ÷ 4 = 2,400 m = 2 km 400 m per day.
🌳 Part 5: Estimating, and Inches and Feet
To guess the height of a tall thing, use a “reference” you know. One floor of a house is about 3 m. So a 4-floor building is about 4 × 3 = 12 m tall.
Heights of people are often said in feet and inches:
- 1 inch is about 2 cm 5 mm (2.5 cm)
- 1 foot = 12 inches, about 30 cm
A child who is 4 feet 6 inches tall is about 120 + 15 = 135 cm.
❌ Common Mistakes to Avoid
✅ Change to the same unit first: 340 cm.
✅ Start from the 0 mark.
✅ 1 km = 1,000 m.
✅ Change 100 cm into 1 m: 6 m 30 cm.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Page 57 · Let Us FindRight units
Double number line: 100 cm, 200 cm, 400 cm, 500 cm, 700 cm → 1 m, 2 m, 4 m, 5 m, 7 m
Match the saris and stoles
Rods and statues
Q2: (a) 182 − 93 = 89 m (b) Statue of Liberty (93 m) and The Motherland Calls (91 m): only 2 m apart (c) Statue of Unity (182 m) and Christ the Redeemer (38 m): 144 m apart (d) The Motherland Calls, since 91 × 2 = 182
Steps and ropes
Ropes to make 1 km: 100 m → 10 · 10 m → 100 · 200 m → 5 · 500 m → 2 · 250 m → 4
3-km race arrangements
Q2: At 300 m, 600 m, 900 m … 2,700 m → 9 children (10 if one also stands at the finish line)
Q3: 3,000 ÷ 50 = 60 flags from 50 m to 3,000 m → 30 red and 30 blue
Longest train journey
Millimetres, sprouts, and drawing
To draw 36 mm, think 3 cm 6 mm. For 67 mm, think 6 cm 7 mm.
Double number lines
(b) 1 m = 100 cm · 4 m = 400 cm · 10 m = 1,000 cm · 12 m = 1,200 cm · 14 m · 17 m · 21 m = 2,100 cm
(c) 9 km = 9,000 m · 25 km = 25,000 m · 41 km · 55 km · 67 km · 82 km = 82,000 m
Conversions
Ribbons, waterfalls, and gondolas
Q2: 48 km 700 m − 17 km 900 m = 30 km 800 m
Q3: 2 km 300 m + 2 km 650 m = 4 km 950 m
Q4: (a) 11 mm, 1 mm (b) 26 mm, 6 mm (c) 201 mm, 1 mm (d) 1,020 mm, 20 mm (e) 245 cm, 45 cm (f) 6 km, 322 m (g) 6 km 1,480 m = 7 km 480 m, so it is bigger by 1 m
Cloth, thread, and roads
Q3: 5 m = 10 × 50 cm, so she needs 10 × 1 m = 10 m of thread. Cost = 10 × ₹50 = ₹500
Q4: 12 km 600 m = 12,600 m. 12,600 ÷ 6 = 2,100 m = 2 km 100 m per day
Heights and the sign puzzle
Sign puzzle:
| ÷ | − | × | + |
| + | × | − | ÷ |
| − | ÷ | + | × |
| × | + | ÷ | − |
👨👩👧 Tips for Parents
- Measure family members’ heights on a wall and write them in cm and in feet/inches.
- Use a phone map to check distances to school, the market, and relatives’ homes in km.
- When buying cloth or lace, ask your child to work out the cost per metre.