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Measurement of Length

NCERT Class 5 · Mathematics Based on NCERT Class 5 Mathematics textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter builds on earlier learning about measuring length and introduces standard units like millimetre (mm), centimetre (cm), metre (m), and kilometre (km). It explains the relationships between these units and how to convert, add, subtract, multiply, and divide lengths in real-life contexts. The big idea is that measuring length accurately requires choosing the right unit and applying conversions correctly, which is essential for everyday tasks like buying cloth, planning a race, or estimating distances.
Key Concepts (12)
Millimetre (mm)
A unit of length used to measure very small objects. 1 cm = 10 mm.
e.g. The length of a sprout from a moong seed is measured in millimetres.
Centimetre (cm)
A unit of length used to measure small to medium objects. 1 cm = 10 mm, 100 cm = 1 m.
e.g. The length of a mobile phone is about 13 cm.
Metre (m)
A standard unit of length used for measuring medium distances. 1 m = 100 cm, 1000 m = 1 km.
e.g. The height of India Gate is 42 m.
Kilometre (km)
A unit used to measure long distances. 1 km = 1000 m. 'Kilo' means thousand.
e.g. The distance from Dibrugarh to Kanniyakumari is 4187 km.
Inch
A non-standard unit of length. 1 inch = 2 cm 5 mm (approximately 2.5 cm).
e.g. Height of a person is often measured in feet and inches.
Foot
A non-standard unit of length. 1 foot = 12 inches or approximately 30 cm.
e.g. The height of an electric pole is often given in feet.
Double number line
A visual tool used to show equivalent measures in two different units, e.g., cm and m, or m and km.
e.g. A double number line shows 1 m = 100 cm, 2 m = 200 cm, etc.
Conversion
Changing a measurement from one unit to another without changing the actual length.
e.g. Converting 5 m 40 cm to 540 cm.
Addition of lengths
Adding lengths by aligning same units (mm with mm, cm with cm, m with m, km with km) and carrying over when needed.
e.g. 3 km 450 m + 4 km 650 m = 8 km 100 m.
Subtraction of lengths
Subtracting lengths by borrowing from a larger unit when necessary.
e.g. 63 m - 16 m 75 cm = 46 m 25 cm.
Multiplication of lengths
Multiplying a length by a number, often by converting to a smaller unit first or breaking into m and cm.
e.g. 20 × 1 m 80 cm = 20 m + 1600 cm = 36 m.
Division of lengths
Dividing a total length into equal parts.
e.g. 12 km 600 m ÷ 6 = 2 km 100 m per day.
Formulas & Equations (5)
1 cm = 10 mm
Reads as: One centimetre equals ten millimetres.
Variables: cm = centimetre, mm = millimetre
Use when: Converting a length from centimetres to millimetres or vice versa.
⚠ Students write 1 cm = 100 mm instead of 10 mm.
100 cm = 1 m
Reads as: One hundred centimetres equals one metre.
Variables: cm = centimetre, m = metre
Use when: Converting between centimetres and metres.
⚠ Students think 1 m = 10 cm instead of 100 cm.
1000 m = 1 km
Reads as: One thousand metres equals one kilometre.
Variables: m = metre, km = kilometre
Use when: Converting between metres and kilometres.
⚠ Students write 1 km = 100 m instead of 1000 m.
1 inch = 2 cm 5 mm (approximately 2.5 cm)
Reads as: One inch equals two centimetres and five millimetres.
Variables: inch = inch, cm = centimetre, mm = millimetre
Use when: Converting inches to centimetres or vice versa.
⚠ Students forget the 5 mm part and write 1 inch = 2 cm exactly.
1 foot = 12 inches or approximately 30 cm
Reads as: One foot equals twelve inches or approximately thirty centimetres.
Variables: foot = foot, inch = inch, cm = centimetre
Use when: Converting feet to inches or centimetres.
⚠ Students think 1 foot = 10 inches.
How It Works
Converting between units using a double number line
  1. Step 1: Draw two parallel lines. Label the top line with one unit (e.g., cm) and the bottom line with the equivalent unit (e.g., m).
  2. Step 2: Mark the known equivalent pair (e.g., 1 m = 100 cm).
  3. Step 3: Multiply both sides by the same number to find other equivalent pairs.
  4. Step 4: Read off the required conversion from the number line.
💡 Always multiply or divide both sides of the number line by the same number to keep the relationship correct.
Adding lengths with different units
  1. Step 1: Write the lengths aligning same units (km with km, m with m, cm with cm, mm with mm).
  2. Step 2: Add each column starting from the smallest unit.
  3. Step 3: If a column sum exceeds the conversion limit (e.g., 100 cm = 1 m), carry over to the next higher unit.
  4. Step 4: Write the final answer in the largest appropriate unit.
💡 Always check if the sum of smaller units can be converted to a larger unit — e.g., 1100 m = 1 km 100 m.
Subtracting lengths with borrowing
  1. Step 1: Write the lengths aligning same units.
  2. Step 2: If a smaller unit in the subtrahend is larger than the corresponding unit in the minuend, borrow 1 from the next higher unit (e.g., borrow 1 m = 100 cm).
  3. Step 3: Subtract each column.
  4. Step 4: Write the answer in the largest appropriate unit.
💡 When borrowing from metres, add 100 to the centimetres column, not 10.
Multiplying a length by a number
  1. Step 1: Break the length into larger and smaller units (e.g., 1 m 80 cm = 1 m + 80 cm).
  2. Step 2: Multiply each part by the given number.
  3. Step 3: Convert the smaller unit result into the larger unit if needed (e.g., 1600 cm = 16 m).
  4. Step 4: Add the results to get the final length.
💡 Alternatively, convert the entire length to the smallest unit first (e.g., 1 m 80 cm = 180 cm), multiply, then convert back.
Dividing a length into equal parts
  1. Step 1: Convert the total length into the smallest unit involved (e.g., 12 km 600 m = 12,600 m).
  2. Step 2: Divide by the number of parts.
  3. Step 3: Convert the result back into the largest appropriate unit (e.g., 2100 m = 2 km 100 m).
💡 If the division does not give a whole number, express the remainder in the smaller unit.
Exam Traps — Don't Make These Mistakes
⚠ Confusing cm and mm conversion
✗ 1 cm = 100 mm
→ 1 cm is divided into 10 equal parts, each 1 mm, so 1 cm = 10 mm, not 100.
✓ 1 cm = 10 mm
⚠ Forgetting to convert before comparing
✗ 456 cm > 5 m because 456 is bigger than 5
→ Units are different; you must convert 5 m to 500 cm before comparing. 456 cm < 500 cm.
✓ Convert 5 m = 500 cm, then 456 cm < 500 cm, so 456 cm < 5 m.
⚠ Wrong borrowing in subtraction of lengths
✗ 63 m - 16 m 75 cm = 47 m 25 cm (borrowing 1 m as 10 cm)
→ When borrowing 1 m, you must add 100 cm, not 10 cm, to the centimetres column.
✓ Borrow 1 m = 100 cm, so 63 m = 62 m 100 cm. Then 62 m 100 cm - 16 m 75 cm = 46 m 25 cm.
⚠ Incorrect addition carrying over
✗ 3 km 450 m + 4 km 650 m = 7 km 1100 m
→ 1100 m should be converted to 1 km 100 m because 1000 m = 1 km.
✓ 3 km 450 m + 4 km 650 m = 7 km 1100 m = 8 km 100 m.
⚠ Mixing up km and m in division
✗ 12 km 600 m ÷ 6 = 2 km 100 m (without converting)
→ While the answer is correct here, students often forget to convert when the division does not give whole km. The safe method is to convert to metres first.
✓ Convert 12 km 600 m = 12,600 m. Then 12,600 m ÷ 6 = 2100 m = 2 km 100 m.
Compare & Contrast
Size of unit
Centimetre (cm)
Millimetre (mm)
1 cm = 10 mm, so a centimetre is ten times larger than a millimetre. Use cm for objects like a mobile phone, and mm for very small objects like a sprout or a nail.
Distance measured
Metre (m)
Kilometre (km)
1 km = 1000 m, so a kilometre is one thousand times larger than a metre. Use m for medium distances like the height of a building, and km for long distances like the journey between cities.
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks), 1 LA (5 marks) — total 10 marks
Most asked: Conversion between units (mm, cm, m, km) · Addition and subtraction of lengths with borrowing/carrying · Comparing lengths using <, =, > after conversion · Word problems involving multiplication and division of lengths
Don't skip: Word problems on adding or subtracting lengths with conversion (e.g., total distance walked, cloth needed); Comparing lengths after converting to the same unit
One-Line Revision (read aloud before the exam)
  1. 1 cm = 10 mm, 100 cm = 1 m, 1000 m = 1 km.
  2. To compare lengths, always convert to the same unit first.
  3. When adding lengths, add same units together and carry over if needed (e.g., 100 cm = 1 m, 1000 m = 1 km).
  4. When subtracting lengths, borrow 1 m = 100 cm, not 10 cm.
  5. To multiply a length, break into m and cm or convert entirely to cm.
  6. To divide a length, convert to the smallest unit first.
  7. A double number line helps visualise equivalent measures between two units.
  8. 1 inch = 2 cm 5 mm (approximately 2.5 cm).
  9. 1 foot = 12 inches or approximately 30 cm.
  10. The Statue of Unity in India is 182 m tall.
  11. The longest train journey in India is from Dibrugarh to Kanniyakumari, 4187 km.
  12. Kilo means thousand, so 1 kilometre = 1000 metres.
  13. For a 3 km race with water stations every 500 m, you need 6 water stations (at 500 m, 1000 m, 1500 m, 2000 m, 2500 m, 3000 m).

MCQs — 10 Questions with Answers

Q1. How many millimetres are there in 5 centimetres?

  • A. 5 mm
  • B. 50 mm ✓
  • C. 500 mm
  • D. 5,000 mm

Answer: B — Since 1 cm = 10 mm, then 5 cm = 5 × 10 = 50 mm.

Q2. Fill in the blank: 1 kilometre = _______ metres.

  • A. 10 m
  • B. 100 m
  • C. 1,000 m ✓
  • D. 10,000 m

Answer: C — By definition from the chapter, 1 km = 1,000 m because kilo means thousand.

Q3. Convert 234 centimetres into millimetres.

  • A. 234 mm
  • B. 2,340 mm ✓
  • C. 23.4 mm
  • D. 2,34 mm

Answer: B — To convert cm to mm, multiply by 10: 234 × 10 = 2,340 mm.

Q4. Which is larger: 456 cm or 5 m?

  • A. 456 cm is larger
  • B. 5 m is larger ✓
  • C. They are equal
  • D. Cannot be compared

Answer: B — Convert to same unit: 5 m = 500 cm, and 500 cm > 456 cm, so 5 m is larger.

Q5. Saji walked 3 km 450 m in the morning and 4 km 650 m in the evening. How far did he walk in total?

  • A. 7 km 100 m
  • B. 8 km 100 m ✓
  • C. 7 km 1,100 m
  • D. 8 km 50 m

Answer: B — Add km and m separately: 3 + 4 = 7 km, and 450 + 650 = 1,100 m = 1 km 100 m, so total = 8 km 100 m.

Q6. What does 89 mm equal when written in cm and mm?

  • A. 8 cm 9 mm ✓
  • B. 9 cm 8 mm
  • C. 0 cm 89 mm
  • D. 80 cm 9 mm

Answer: A — Since 10 mm = 1 cm, divide: 89 ÷ 10 = 8 remainder 9, so 89 mm = 8 cm 9 mm.

Q7. India Gate is 42 metres tall. How many centimetres is this?

  • A. 4.2 cm
  • B. 420 cm
  • C. 4,200 cm ✓
  • D. 42,000 cm

Answer: C — To convert metres to centimetres, multiply by 100: 42 × 100 = 4,200 cm.

Q8. The distance between two buttons on a shirt is 5 cm. How many millimetres is this?

  • A. 0.5 mm
  • B. 5 mm
  • C. 50 mm ✓
  • D. 500 mm

Answer: C — Since 1 cm = 10 mm, multiply: 5 × 10 = 50 mm.

Q9. Which measurement could represent the height of a house?

  • A. 5 cm
  • B. 5 mm
  • C. 50 m ✓
  • D. 5,000 km

Answer: C — A typical house is about 15-20 metres tall, so 50 m is a reasonable height for a taller building, while cm and mm are too small and km is far too large.

Q10. Convert 5,792 cm into metres and centimetres.

  • A. 57 m 92 cm ✓
  • B. 579 m 2 cm
  • C. 5 m 792 cm
  • D. 57.92 m only

Answer: A — Divide by 100: 5,792 ÷ 100 = 57 with remainder 92, so 5,792 cm = 57 m 92 cm.

Flashcards

What does 1 mm mean?

1 millimetre is one tenth of a centimetre, used to measure very small things like the thickness of a coin.

How many millimetres are in 1 centimetre?

1 cm = 10 mm (ten millimetres equal one centimetre).

What is the relationship between metre and centimetre?

1 m = 100 cm (one hundred centimetres equal one metre).

What does 1 km equal?

1 km = 1,000 m (one kilometre equals one thousand metres, used for long distances like between cities).

Convert 45 mm to cm and mm.

45 mm = 4 cm 5 mm (because 40 mm = 4 cm and 5 mm remains).

How do you add 3 km 450 m and 4 km 650 m?

Add the kilometres together (3 + 4 = 7 km) and metres together (450 + 650 = 1,100 m), then convert 1,100 m to 1 km 100 m, giving 8 km 100 m.

Convert 6 m 34 cm into only centimetres.

6 m 34 cm = 634 cm (because 6 m = 600 cm, so 600 + 34 = 634 cm).

What tools can measure long distances?

Long tape, rodometer (measuring wheel), rangefinder, and laser distance meter are tools used to measure long distances.

When comparing 456 cm and 5 m, which is larger?

5 m is larger because 5 m = 500 cm, and 500 cm > 456 cm, so 456 cm < 5 m.

What is the total distance of The Vivek Express train journey?

The Vivek Express journey from Dibrugarh to Kanniyakumari is 4,187 km long.

Important Board Questions

What is 1 millimetre and why do we need it? [1 mark]

1 mm is one tenth of a centimetre, used when measuring very small objects like nails or screws where cm is not precise enough.

Fill in the blanks: (a) 1 m = _____ cm (b) 1 km = _____ m [2 marks]

Use the conversion relationships from the chapter: centimetres are 100 times smaller than metres, and metres are 1,000 times smaller than kilometres.

Explain with an example from your daily life why we need different units of measurement like mm, cm, m, and km. [3 marks]

Use examples such as: mm for measuring the thickness of a coin, cm for measuring pencil length, m for measuring classroom size, and km for measuring distance between cities. Show that using the wrong unit makes measurement confusing.

The Vivek Express train journey has 8 stations listed. Station 1 (Dimapur) is 306 km from Dibrugarh, and Station 8 (Kanniyakumari) is 4,187 km from Dibrugarh. (a) What is the distance between these two stations? (b) If a person travels from Guwahati (556 km) to Visakhapatnam (2,450 km), how far do they travel? (c) Explain how you solved part (b). [5 marks]

Part (a): Subtract the starting distance from the ending distance (4,187 − 306 = 3,881 km). Part (b): Use the same method (2,450 − 556 = 1,894 km). Part (c): Explain that when distances are given from the same starting point, we subtract the smaller from the larger to find the distance between two places.

True or False: 3 km 450 m + 4 km 650 m = 7 km 1,100 m. Explain your answer. [2 marks]

The addition is correct (3 + 4 = 7 km, 450 + 650 = 1,100 m), but the final answer must be simplified because 1,100 m = 1 km 100 m, so the true answer is 8 km 100 m.

Assertion-Reason Questions for Measurement of Length

Q1. Assertion (A):

Centimetre is a larger unit than millimetre.

Reason (R):

1 centimetre equals 10 millimetres.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true. Since 1 cm = 10 mm, centimetre is indeed larger, and the reason correctly explains why. The reason is the correct explanation.

Q2. Assertion (A):

To measure the distance between two cities, we use metres as the unit.

Reason (R):

Metres are used for short distances like room length.

Answer: D — A is false but R is true — The assertion is false because distances between cities are measured in kilometres, not metres. The reason is true but does not support the assertion. For long distances like between cities, we use km.

Q3. Assertion (A):

The conversion 1,000 m = 1 km is a standard relationship used in measurement.

Reason (R):

Kilo means thousand, so 1 km means 1,000 metres.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains the assertion. The prefix 'kilo' stands for 'thousand', which is why 1 km = 1,000 m.

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Case-Based Questions (CBQ) for Measurement of Length

Case Study:

Priya is preparing a vegetable garden at home. She measures the length of her garden plot as 12 m 50 cm. She decides to plant tomatoes along a 4 m 75 cm section and spinach along a 3 m 50 cm section. The remaining space will have carrots. She also marks every 1 m 50 cm with a small flag to separate different planting areas.

Q1. What is the total length of the tomato and spinach sections combined?

  • A. 8 m 25 cm ✓
  • B. 7 m 25 cm
  • C. 9 m 50 cm
  • D. 8 m 75 cm

Answer: A

Q2. How much space is left for carrots?

  • A. 4 m 50 cm ✓
  • B. 4 m 75 cm
  • C. 3 m 75 cm
  • D. 5 m 25 cm

Answer: A

Q3. If Priya places flags every 1 m 50 cm, how many 1 m 50 cm sections will she have in her entire 12 m 50 cm garden?

  • A. 8 sections ✓
  • B. 10 sections
  • C. 9 sections
  • D. 12 sections

Answer: A

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