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Weight and Capacity

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

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Chapter Notes

Overview
This chapter introduces students to the measurement of weight and capacity, focusing on standard units like grams (g), kilograms (kg), milligrams (mg), millilitres (ml), and litres (l). It explains how to read weighing scales, convert between units, and perform addition, subtraction, multiplication, and division on quantities. The one big idea is that all measurements can be converted to a common unit (e.g., grams or millilitres) to simplify calculations, and that real-life problems require careful handling of mixed units.
Key Concepts (16)
Gram (g)
A unit of weight used to measure light objects.
e.g. A water bottle weighs 650 g.
Kilogram (kg)
A unit of weight equal to 1000 grams, used for heavier objects.
e.g. A bed weighs 60 kg.
Milligram (mg)
A unit of weight equal to 1/1000 of a gram, used for very light objects.
e.g. An ant weighs between 1 mg and 5 mg.
Quintal
A unit of weight equal to 100 kilograms.
e.g. 100 kg = 1 quintal.
Tonne
A unit of weight equal to 1000 kilograms or 10 quintals.
e.g. 1000 kg = 1 tonne.
Litres (l)
A unit of capacity used to measure liquids.
e.g. A bucket can hold 20 l of water.
Millilitres (ml)
A unit of capacity equal to 1/1000 of a litre.
e.g. A water bottle holds 500 ml.
Conversion between kg and g
1 kg = 1000 g. To convert kg to g, multiply by 1000. To convert g to kg, divide by 1000.
e.g. 3 kg 500 g = 3500 g.
Conversion between g and mg
1 g = 1000 mg. To convert g to mg, multiply by 1000. To convert mg to g, divide by 1000.
e.g. 4 g 100 mg = 4100 mg.
Conversion between l and ml
1 l = 1000 ml. To convert l to ml, multiply by 1000. To convert ml to l, divide by 1000.
e.g. 2 l = 2000 ml.
Addition of weights
Adding quantities of weight by aligning kg and g separately, then converting if g exceeds 1000.
e.g. 2 kg 500 g + 1 kg 750 g = 4 kg 250 g.
Subtraction of weights
Subtracting quantities of weight by aligning kg and g, borrowing 1 kg = 1000 g if needed.
e.g. 2 kg 500 g - 1 kg 750 g = 750 g.
Multiplication of weights
Multiplying a weight by a whole number by multiplying kg and g separately, then converting.
e.g. 4 × 10 kg 500 g = 42 kg.
Division of weights
Dividing a weight by a whole number by converting to grams first or dividing kg and g separately.
e.g. 4 kg 800 g ÷ 4 = 1 kg 200 g.
Addition of capacities
Adding quantities of capacity by aligning l and ml separately, then converting if ml exceeds 1000.
e.g. 2 l 500 ml + 2 l 800 ml = 5 l 300 ml.
Subtraction of capacities
Subtracting quantities of capacity by aligning l and ml, borrowing 1 l = 1000 ml if needed.
e.g. 9 l - 5 l 300 ml = 3 l 700 ml.
Formulas & Equations (6)
1 kg = 1000 g
Reads as: One kilogram equals one thousand grams.
Variables: kg = kilogram, g = gram
Use when: Converting between kilograms and grams in any problem.
⚠ Students write 1 kg = 100 g instead of 1000 g.
1 g = 1000 mg
Reads as: One gram equals one thousand milligrams.
Variables: g = gram, mg = milligram
Use when: Converting between grams and milligrams.
⚠ Students confuse mg with g and write 1 g = 100 mg.
1 l = 1000 ml
Reads as: One litre equals one thousand millilitres.
Variables: l = litre, ml = millilitre
Use when: Converting between litres and millilitres.
⚠ Students write 1 l = 100 ml instead of 1000 ml.
100 kg = 1 quintal
Reads as: One hundred kilograms equals one quintal.
Variables: kg = kilogram, quintal = quintal
Use when: Converting between kilograms and quintals.
⚠ Students think 1 quintal = 1000 kg.
10 quintals = 1 tonne
Reads as: Ten quintals equals one tonne.
Variables: quintal = quintal, tonne = tonne
Use when: Converting between quintals and tonnes.
⚠ Students confuse tonne with quintal.
1000 kg = 1 tonne
Reads as: One thousand kilograms equals one tonne.
Variables: kg = kilogram, tonne = tonne
Use when: Converting between kilograms and tonnes.
⚠ Students write 100 kg = 1 tonne.
How It Works
Reading a weighing scale
  1. Step 1: Observe the scale and note the markings (e.g., kg, g, or both).
  2. Step 2: Identify where the pointer or needle stops.
  3. Step 3: Read the value in the given unit (e.g., 3 kg 500 g).
  4. Step 4: If the scale has sub-divisions, count the smaller marks to get precise grams.
💡 Always check where the '0' is on the scale — some scales start from 0, others have a different baseline.
Converting kg to g and g to kg
  1. Step 1: To convert kg to g, multiply the number of kg by 1000.
  2. Step 2: Add any extra grams if given (e.g., 3 kg 500 g = 3000 g + 500 g = 3500 g).
  3. Step 3: To convert g to kg, divide the number of g by 1000.
  4. Step 4: The quotient is kg, the remainder is g (e.g., 3500 g = 3 kg 500 g).
💡 Students often forget to add the extra grams after converting kg — always add them.
Converting g to mg and mg to g
  1. Step 1: To convert g to mg, multiply the number of g by 1000.
  2. Step 2: Add any extra mg if given (e.g., 4 g 100 mg = 4000 mg + 100 mg = 4100 mg).
  3. Step 3: To convert mg to g, divide the number of mg by 1000.
  4. Step 4: The quotient is g, the remainder is mg (e.g., 4100 mg = 4 g 100 mg).
💡 Do not confuse mg with g — 1 g = 1000 mg, not 100 mg.
Converting l to ml and ml to l
  1. Step 1: To convert l to ml, multiply the number of l by 1000.
  2. Step 2: Add any extra ml if given (e.g., 2 l 500 ml = 2000 ml + 500 ml = 2500 ml).
  3. Step 3: To convert ml to l, divide the number of ml by 1000.
  4. Step 4: The quotient is l, the remainder is ml (e.g., 2500 ml = 2 l 500 ml).
💡 Always write the remainder as ml, not as a decimal of l unless asked.
Adding weights or capacities (column method)
  1. Step 1: Write the quantities in columns — kg and g (or l and ml) aligned.
  2. Step 2: Add the grams (or ml) column first.
  3. Step 3: If the sum of grams (or ml) is 1000 or more, convert 1000 units into 1 kg (or 1 l) and carry over.
  4. Step 4: Add the kg (or l) column including the carry-over.
  5. Step 5: Write the final answer in kg and g (or l and ml).
💡 Never write 1500 g in the answer — always convert to 1 kg 500 g.
Subtracting weights or capacities (column method)
  1. Step 1: Write the quantities in columns — kg and g (or l and ml) aligned.
  2. Step 2: If the grams (or ml) in the subtrahend are larger, borrow 1 kg (or 1 l) = 1000 g (or 1000 ml) from the kg (or l) column.
  3. Step 3: Subtract the grams (or ml) column.
  4. Step 4: Subtract the kg (or l) column.
  5. Step 5: Write the final answer in kg and g (or l and ml).
💡 When borrowing, reduce the kg (or l) by 1 and add 1000 to the g (or ml) column.
Multiplying weights or capacities
  1. Step 1: Multiply the kg (or l) part by the multiplier.
  2. Step 2: Multiply the g (or ml) part by the multiplier.
  3. Step 3: If the product in g (or ml) is 1000 or more, convert to kg (or l).
  4. Step 4: Add the converted part to the kg (or l) product.
  5. Step 5: Write the final answer.
💡 Alternatively, convert everything to grams (or ml) first, multiply, then convert back.
Dividing weights or capacities
  1. Step 1: Convert the total weight (or capacity) into grams (or ml).
  2. Step 2: Divide the total grams (or ml) by the divisor.
  3. Step 3: Convert the quotient back to kg and g (or l and ml) by dividing by 1000.
  4. Step 4: Write the final answer.
💡 If the division is not exact, the remainder is in grams (or ml) — do not drop it.
Using double number line for conversions
  1. Step 1: Draw two parallel lines — one for the larger unit (e.g., kg), one for the smaller unit (e.g., g).
  2. Step 2: Mark known equivalent pairs (e.g., 1 kg = 1000 g).
  3. Step 3: Use multiplication or division to find missing values (e.g., 3 kg = 3000 g).
  4. Step 4: Fill in the blanks by following the pattern.
💡 The double number line shows the relationship — always multiply or divide both sides by the same number.
Exam Traps — Don't Make These Mistakes
⚠ Confusing grams and kilograms in real-life estimates
✗ Iron Almirah – 40 g
→ An iron almirah is heavy — it should be measured in kilograms, not grams. 40 g is the weight of a small chocolate, not a cupboard.
✓ Iron Almirah – 40 kg
⚠ Incorrect conversion of 5 kg 50 g to grams
✗ 5 kg 50 g = 5500 g
→ 5 kg = 5000 g, plus 50 g gives 5050 g, not 5500 g. The student mistakenly added 500 g instead of 50 g.
✓ 5 kg 50 g = 5050 g
⚠ Confusing 1 l 400 ml with 1 l 40 ml
✗ 1 l 400 ml = 1040 ml
→ 1 l = 1000 ml, plus 400 ml gives 1400 ml, not 1040 ml. The student wrote 40 ml instead of 400 ml.
✓ 1 l 400 ml = 1400 ml
⚠ Forgetting to convert 1000 g to 1 kg in addition
✗ 2 kg 500 g + 1 kg 750 g = 3 kg 1250 g
→ 1250 g is more than 1000 g — it must be converted to 1 kg 250 g and added to the kg column.
✓ 2 kg 500 g + 1 kg 750 g = 4 kg 250 g
⚠ Incorrect subtraction when borrowing is needed
✗ 2 kg 500 g - 1 kg 750 g = 1 kg 250 g
→ 500 g - 750 g is not possible without borrowing. The student subtracted 500 from 750 incorrectly.
✓ 2 kg 500 g - 1 kg 750 g = 750 g (borrow 1 kg = 1000 g, then 1500 g - 750 g = 750 g)
⚠ Confusing mg with g in comparison
✗ 20 g > 200 mg (correct, but they write 20 g = 200 mg)
→ 20 g = 20,000 mg, which is much larger than 200 mg. Students often think 1 g = 100 mg.
✓ 20 g > 200 mg (since 20 g = 20,000 mg)
Compare & Contrast
Unit of weight
Kilogram (kg)
Gram (g)
1 kg = 1000 g; kg is used for heavier objects (e.g., a bag of rice), while g is used for lighter objects (e.g., a water bottle).
Unit of capacity
Litres (l)
Millilitres (ml)
1 l = 1000 ml; l is used for larger volumes (e.g., a bucket of water), while ml is used for smaller volumes (e.g., a spoon of medicine).
Unit of weight for bulk goods
Quintal
Tonne
1 tonne = 10 quintals = 1000 kg; quintal is used for moderate bulk (e.g., a sack of grain), tonne for very heavy loads (e.g., a truckload of sand).
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks) on conversions, 1 LA (5 marks) on addition/subtraction word problem
Most asked: Conversion between kg and g · Conversion between l and ml · Addition and subtraction of weights and capacities · Reading weighing scales · Word problems involving real-life scenarios (e.g., grocery, milk delivery, petrol pump)
Don't skip: Word problems requiring addition or subtraction of mixed units (e.g., kg and g, l and ml) with borrowing or carrying; Conversion problems that ask to express a quantity in a different unit
One-Line Revision (read aloud before the exam)
  1. 1 kg = 1000 g.
  2. 1 g = 1000 mg.
  3. 1 l = 1000 ml.
  4. 100 kg = 1 quintal.
  5. 10 quintals = 1 tonne.
  6. 1000 kg = 1 tonne.
  7. To convert kg to g, multiply by 1000.
  8. To convert g to kg, divide by 1000.
  9. To convert l to ml, multiply by 1000.
  10. To convert ml to l, divide by 1000.
  11. When adding weights, always convert 1000 g to 1 kg.
  12. When subtracting weights, borrow 1 kg = 1000 g if needed.
  13. When adding capacities, always convert 1000 ml to 1 l.
  14. When subtracting capacities, borrow 1 l = 1000 ml if needed.
  15. A double number line helps to see the relationship between units.
  16. Always check the unit before comparing weights or capacities.

MCQs — 10 Questions with Answers

Q1. How many grams are there in 4 kg?

  • A. 400 g
  • B. 4,000 g ✓
  • C. 40,000 g
  • D. 4 g

Answer: B — To convert kilograms to grams, multiply by 1,000, so 4 kg = 4 × 1,000 = 4,000 g.

Q2. Which object's weight is recorded correctly?

  • A. Iron almirah = 40 kg
  • B. Sofa = 30 g
  • C. Refrigerator = 50 g
  • D. Rice bag = 5 kg ✓

Answer: D — A rice bag of 5 kg is correct; the almirah, sofa, and refrigerator are much heavier than 40g, 30g, and 50g respectively.

Q3. What is 6 kg 750 g expressed in grams?

  • A. 675 g
  • B. 6,075 g
  • C. 6,750 g ✓
  • D. 67,500 g

Answer: C — Convert 6 kg to grams (6,000 g) and add 750 g: 6,000 g + 750 g = 6,750 g.

Q4. If 1 kg = 1,000 g, how many kilograms is 9,000 g?

  • A. 90 kg
  • B. 900 kg
  • C. 9 kg ✓
  • D. 0.9 kg

Answer: C — To convert grams to kilograms, divide by 1,000: 9,000 g ÷ 1,000 = 9 kg.

Q5. What is the total weight when 3 kg 200 g and 2 kg 800 g are added?

  • A. 5 kg
  • B. 6 kg ✓
  • C. 5 kg 800 g
  • D. 6 kg 200 g

Answer: B — 3 kg + 2 kg = 5 kg, and 200 g + 800 g = 1,000 g = 1 kg, so total is 5 kg + 1 kg = 6 kg.

Q6. Which is heavier: 7 kg 200 g or 7,200 g?

  • A. 7 kg 200 g is heavier
  • B. 7,200 g is heavier
  • C. Both are equal ✓
  • D. Cannot be determined

Answer: C — 7 kg 200 g = 7,000 g + 200 g = 7,200 g, so both are equal in weight.

Q7. How much is 8 g in milligrams?

  • A. 80 mg
  • B. 800 mg
  • C. 8,000 mg ✓
  • D. 80,000 mg

Answer: C — To convert grams to milligrams, multiply by 1,000: 8 g = 8 × 1,000 = 8,000 mg.

Q8. If the king donates 800 kg of wheat and this equals 10 times his weight, what is his weight?

  • A. 80 kg ✓
  • B. 800 kg
  • C. 8,000 kg
  • D. 100 kg

Answer: A — If 10 times his weight = 800 kg, then his weight = 800 kg ÷ 10 = 80 kg.

Q9. What is 1 tonne equal to in kilograms?

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

Answer: C — 1 tonne = 1,000 kg, which is the standard conversion for the heaviest weight unit.

Q10. Rathna bought 2 kg 500 g rice for daily use and 1 kg 750 g for Pongal. How much total rice did she buy?

  • A. 3 kg 250 g
  • B. 4 kg 250 g ✓
  • C. 3 kg 1,250 g
  • D. 4 kg 500 g

Answer: B — Add separately: 2 kg + 1 kg = 3 kg, and 500 g + 750 g = 1,250 g = 1 kg 250 g, so total is 4 kg 250 g.

Flashcards

What is the relationship between kilograms and grams?

1 kilogram (kg) equals 1,000 grams (g), so to convert kg to g, multiply by 1,000.

How do you convert 3 kg 500 g to grams only?

3 kg 500 g = 3,000 g + 500 g = 3,500 g (multiply the kg by 1,000 and add the grams).

What is a milligram and when is it used?

A milligram (mg) is a very small unit of weight; 1 gram = 1,000 milligrams, used for light things like medicine or gold ornaments.

How do you add weights like 2 kg 500 g + 1 kg 750 g?

Group the kilograms and grams separately: 2 kg + 1 kg = 3 kg, and 500 g + 750 g = 1 kg 250 g, so total is 4 kg 250 g.

What is the difference between a quintal and a tonne?

1 quintal = 100 kg, and 1 tonne = 10 quintals = 1,000 kg, so a tonne is 10 times heavier than a quintal.

How do you read a weighing scale correctly?

Always find where the pointer is pointing and read from the zero mark on that particular scale.

Convert 10 g 500 mg into milligrams only.

10 g 500 mg = 10,000 mg + 500 mg = 10,500 mg (multiply g by 1,000 and add the mg).

Which unit should you use to weigh rice for cooking at home?

You should use kilograms (kg) or grams (g), like 2 kg 500 g of rice, because rice is not very light.

How do you subtract weights like 10 kg - 4 kg 500 g?

Convert to the same unit (10 kg = 10,000 g), then subtract: 10,000 g - 4,500 g = 5,500 g = 5 kg 500 g.

What does the scale show if an ant weighs 3 milligrams?

The scale shows 3 mg, which is extremely tiny and used only for measuring very light objects like ants or medicine powder.

Important Board Questions

What is 5 kg 250 g in grams? [1 mark]

Convert kg to g by multiplying by 1,000, then add the grams: 5 kg = 5,000 g, plus 250 g.

Fill in the blanks: 1 kg = _____ g and 1 g = _____ mg. Convert 3 kg 500 g into grams. [2 marks]

1 kg = 1,000 g and 1 g = 1,000 mg. For 3 kg 500 g: multiply 3 by 1,000 and add 500.

A fruit stall owner has apples weighing 2 kg 500 g and oranges weighing 3 kg 750 g. What is the total weight of fruit? Explain your method. [3 marks]

Add the kilograms together and the grams together separately: group kg with kg and g with g. When grams exceed 1,000, convert to kg.

A grocery store sells rice in three bags: 5 kg 200 g, 8 kg 900 g, and 12 kg 600 g. (a) Find the total weight of rice. (b) If the storekeeper had 30 kg rice, how much was sold? Show your working step by step. [5 marks]

Part (a): Add all three weights by grouping kg and g separately. Part (b): Subtract the total weight sold from 30 kg by converting to the same unit if needed.

True or False: 4 kg 100 mg = 4,100 g. Give a reason for your answer. [2 marks]

Remember that 1 kg = 1,000 g and 1 g = 1,000 mg. 4 kg 100 mg means 4 kg and 100 milligrams, not 100 grams.

Assertion-Reason Questions for Weight and Capacity

Q1. Assertion (A):

To convert 3 kg into grams, we multiply 3 by 1,000.

Reason (R):

1 kilogram equals 1,000 grams.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true and the reason correctly explains why we multiply by 1,000 when converting kg to g.

Q2. Assertion (A):

An iron almirah should be weighed in kilograms, not grams.

Reason (R):

Grams are used only for very light objects like medicine or gold ornaments.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true. Heavy furniture needs kg, and grams work well for light things. The reason explains why the assertion is correct.

Q3. Assertion (A):

5,000 kg is equal to 5 tonnes.

Reason (R):

1 tonne equals 1,000 kg.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both are true. Since 1 tonne = 1,000 kg, then 5,000 kg ÷ 1,000 = 5 tonnes. The reason correctly explains the assertion.

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Case-Based Questions (CBQ) for Weight and Capacity

Case Study:

Meera's mother is preparing food for a family dinner. She buys 2 kg 500 g of rice from the market. At home, she already has 1 kg 250 g of rice. She plans to use 3 kg of rice for cooking biryani and the rest for making regular rice dishes. How much rice will be left after cooking?

Q1. How much total rice does Meera's mother have after buying more?

  • A. 3 kg 250 g
  • B. 3 kg 750 g ✓
  • C. 4 kg
  • D. 2 kg 500 g

Answer: B

Q2. If she uses 3 kg for biryani, how much rice will be left?

  • A. 750 g ✓
  • B. 1 kg 250 g
  • C. 500 g
  • D. 1 kg

Answer: A

Q3. What is the total rice in grams that Meera's mother has at the beginning?

  • A. 3,250 g
  • B. 3,750 g ✓
  • C. 4,250 g
  • D. 2,500 g

Answer: B

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