Solved Exercises on Mass/Weight (Grams and Kilograms) in Grade 3

Master mass and weight measurement: grams to kilograms conversion, comparing weights, adding weights, and solving word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Converting grams to kilograms
Exercise 1
Convert 2,500 grams to kilograms.
Show your work step by step.
Definition:

Conversion factor: 1 kilogram (kg) = 1,000 grams (g)

Conversion method:
  1. To convert grams to kilograms, divide by 1,000
  2. Move the decimal point 3 places to the left
  3. Express the result in kilograms
Starting amount
2,500 g
Division
2,500 ÷ 1,000
Result
2.5 kg
Step 1: Identify the conversion factor

1 kg = 1,000 g, so to convert from grams to kilograms, divide by 1,000

Step 2: Set up the division

2,500 grams ÷ 1,000 = ? kilograms

Step 3: Perform the calculation

2,500 ÷ 1,000 = 2.5

Step 4: Write the final answer

2,500 grams = 2.5 kilograms

2,500 g = 2.5 kg
Final answer:

2,500 grams equals 2.5 kilograms

Applied rules:

• Conversion factor: 1 kg = 1,000 g

• Division: To convert smaller unit to larger unit, divide

• Decimal placement: Move decimal 3 places left when dividing by 1,000

2 Converting kilograms to grams
Exercise 2
Convert 3.7 kilograms to grams.
Show your work step by step.
Definition:

Conversion factor: 1 kilogram (kg) = 1,000 grams (g)

Starting amount
3.7 kg
Multiplication
3.7 × 1,000
Result
3,700 g
Step 1: Identify the conversion factor

1 kg = 1,000 g, so to convert from kilograms to grams, multiply by 1,000

Step 2: Set up the multiplication

3.7 kilograms × 1,000 = ? grams

Step 3: Perform the calculation

3.7 × 1,000 = 3,700

Step 4: Write the final answer

3.7 kilograms = 3,700 grams

3.7 kg = 3,700 g
Final answer:

3.7 kilograms equals 3,700 grams

Applied rules:

• Conversion factor: 1 kg = 1,000 g

• Multiplication: To convert larger unit to smaller unit, multiply

• Decimal placement: Move decimal 3 places right when multiplying by 1,000

3 Comparing weights
Exercise 3
Which is heavier: 4,500 grams or 4.2 kilograms?
Show your work step by step.
Definition:

Comparison rule: Convert both measurements to the same unit before comparing

First amount
4,500 g
Second amount
4.2 kg = 4,200 g
Comparison
4,500 > 4,200
Step 1: Convert both measurements to the same unit

Convert 4.2 kg to grams: 4.2 × 1,000 = 4,200 grams

Step 2: Compare the two amounts in grams

4,500 grams vs 4,200 grams

Step 3: Determine which is greater

4,500 > 4,200, so 4,500 grams is heavier

Step 4: State the final answer

4,500 grams is heavier than 4.2 kilograms

4,500 g > 4.2 kg
Final answer:

4,500 grams is heavier than 4.2 kilograms

Applied rules:

• Unit conversion: Always convert to same units before comparing

• Comparison: Compare numerical values once units are the same

• Greater than: 4,500 > 4,200 means 4,500 is larger

Key Concepts: Mass/Weight Measurement
1 kg = 1,000 g
Basic Conversion
Grams to Kilograms
÷ 1,000
Divide by 1,000
Kilograms to Grams
× 1,000
Multiply by 1,000
Comparison Rule
Same Units
Convert to same units first
Key definitions:

Mass: The amount of matter in an object

Weight: The force of gravity on an object (measured in same units)

Gram (g): Smaller unit for light objects

Kilogram (kg): Larger unit for heavier objects

Complete methodology:
  1. Identify units: Check what units are given and needed
  2. Choose operation: Multiply when converting to smaller units, divide when converting to larger units
  3. Apply conversion: Use 1 kg = 1,000 g relationship
  4. Calculate: Perform the arithmetic operation
  5. Check: Verify the answer makes sense
Tip 1: Remember: kilo means thousand, so 1 kilogram = 1,000 grams.
Tip 2: When converting from kg to g, move decimal point 3 places right.
Tip 3: When converting from g to kg, move decimal point 3 places left.
Tip 4: Always convert to the same unit before comparing.
Common objects: Apple ≈ 150g, Bag of sugar ≈ 1kg, Person ≈ 30-50kg.
Conversion trick: To divide by 1,000, cross out 3 zeros or move decimal 3 places left.
Essential formulas to remember:

• Conversion: 1 kg = 1,000 g

• Grams to Kilograms: Divide by 1,000

• Kilograms to Grams: Multiply by 1,000

• Comparison: Always convert to same units first

Solution: Exercises 4 to 5
4 Adding weights
Exercise 4
Sarah has 2.5 kg of flour and adds 800 g more. How much flour does she have altogether in kilograms?
Definition:

Addition rule: Convert all measurements to the same unit before adding

First amount
2.5 kg
Second amount
800 g = 0.8 kg
Addition
2.5 + 0.8 = 3.3 kg
Step 1: Convert 800 grams to kilograms

800 g ÷ 1,000 = 0.8 kg

Step 2: Add the two amounts in kilograms

2.5 kg + 0.8 kg = 3.3 kg

Step 3: Verify the calculation

2.5 + 0.8 = 3.3 ✓

Step 4: State the final answer

Sarah has 3.3 kilograms of flour altogether

2.5 kg + 800 g = 3.3 kg
Final answer:

Sarah has 3.3 kilograms of flour altogether

Applied rules:

• Unit conversion: Convert to same units before adding

• Addition: Add numerical values when units are the same

• Conversion factor: 1 kg = 1,000 g

5 Word problem with subtraction
Exercise 5
A bag of rice weighs 5 kg. If 1,250 g of rice is taken out, how much rice is left in grams?
Definition:

Subtraction rule: Convert all measurements to the same unit before subtracting

Original amount
5 kg = 5,000 g
Amount removed
1,250 g
Subtraction
5,000 - 1,250 = 3,750 g
Step 1: Convert 5 kg to grams

5 kg × 1,000 = 5,000 g

Step 2: Subtract the removed amount from total

5,000 g - 1,250 g = 3,750 g

Step 3: Verify the calculation

5,000 - 1,250 = 3,750 ✓

Step 4: State the final answer

There are 3,750 grams of rice left

5 kg - 1,250 g = 3,750 g
Final answer:

There are 3,750 grams of rice left

Applied rules:

• Unit conversion: Convert to same units before subtracting

• Subtraction: Subtract numerical values when units are the same

• Conversion factor: 1 kg = 1,000 g

Complete Guide: Mass/Weight Measurement
1 kg = 1,000 g
Fundamental Conversion
Key definitions:

Mass: The amount of matter in an object, measured in grams (g) or kilograms (kg)

Weight: The force of gravity acting on an object (often used interchangeably with mass in elementary math)

Gram (g): Unit for measuring small masses (like an apple or pencil)

Kilogram (kg): Unit for measuring larger masses (like a bag of rice or person's weight)

Complete methodology:
  1. Identify the problem: Determine what units are given and what units are needed
  2. Choose the operation: Multiply when going from larger unit to smaller unit, divide when going from smaller to larger
  3. Apply conversion factor: Use the relationship 1 kg = 1,000 g
  4. Perform calculations: Carry out the multiplication or division
  5. Verify answer: Check if the answer makes sense in context
Tip 1: Use a conversion chart: kg → g (multiply by 1,000), g → kg (divide by 1,000).
Tip 2: When comparing masses, always convert to the same unit first.
Tip 3: Remember: 1,000 grams = 1 kilogram, just like 1,000 pennies = 10 dollars.
Tip 4: Practice with real objects: weigh fruits, books, or bags to understand mass better.
Real-world examples: Small apple ≈ 150g, Loaf of bread ≈ 500g, Bag of flour ≈ 1kg, Adult ≈ 60-80kg.
Common mistakes: Forgetting to convert units before comparing, mixing up multiplication and division operations.
Essential formulas to know:

• Basic conversion: 1 kg = 1,000 g

• Grams to Kilograms: Divide by 1,000

• Kilograms to Grams: Multiply by 1,000

• Addition/Subtraction: Convert to same units first

• Comparison: Always compare like units

Questions & Answers

Question: I don't understand why we need to convert grams to kilograms or vice versa. Why can't we just keep everything in grams?

Answer: Great question! We use different units for practical reasons:

  • Convenience: It's easier to say "I weigh 35 kg" than "I weigh 35,000 g"
  • Appropriateness: Grams are perfect for small items (like a pencil ≈ 10g), while kilograms are better for larger items (like a backpack ≈ 2kg)
  • Standardization: Grocery stores, hospitals, and many places use specific units

Think of it like measuring distance: you'd measure your height in feet/inches rather than miles, and you'd measure the distance to school in miles rather than inches. Different units make sense for different situations!

Question: When I convert 5,000 grams to kilograms, I get 5.000, but sometimes I see it written as just 5. Are these the same thing?

Answer: Yes, 5.000 and 5 are exactly the same number! The zeros after the decimal point don't change the value.

  • 5.000 = 5.00 = 5.0 = 5
  • It's like having 5 dollars versus 5.00 dollars - they're the same amount
  • In math, we usually write the simplest form, so 5 kg is preferred over 5.000 kg

However, when you have decimals like 5.3 or 2.75, those extra digits DO matter because they represent parts of a whole kilogram.

Question: How do I know whether to multiply or divide when converting between grams and kilograms?

Answer: Think about the size of the units:

  • Going from bigger to smaller unit: Multiply (kilograms → grams)
  • Going from smaller to bigger unit: Divide (grams → kilograms)

Remember: There are 1,000 grams in 1 kilogram, so:

  • 1 kg = 1,000 g (more grams than kilograms)
  • So if you have 3 kg, you'll have MORE grams: 3 × 1,000 = 3,000 g
  • If you have 4,000 g, you'll have FEWER kilograms: 4,000 ÷ 1,000 = 4 kg

The key is: moving to a smaller unit gives you more pieces, so multiply. Moving to a larger unit gives you fewer pieces, so divide.