Solved Exercises on Grams and Kilograms in Grade 3

Master weight measurement: understanding grams and kilograms, conversions, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Conversion: Grams to Kilograms
Exercise 1
A bag of rice weighs 2,500 grams. How many kilograms does it weigh?
Definition:

Gram (g): A unit of weight used to measure light objects.

Kilogram (kg): A unit of weight used to measure heavier objects. 1 kilogram = 1,000 grams.

Conversion Method:
  1. Identify the number of grams to convert
  2. Divide by 1,000 to convert grams to kilograms
  3. Express the result in kilograms
Step 1: Identify the number of grams

Weight of rice = 2,500 grams

Step 2: Apply the conversion formula

Kilograms = Grams ÷ 1,000
Kilograms = 2,500 ÷ 1,000 = 2.5

Step 3: State the result

2,500 grams = 2.5 kilograms

The bag of rice weighs 2.5 kg
Final answer:

The bag of rice weighs 2.5 kilograms.

Applied rules:

• Conversion Factor: 1,000 grams = 1 kilogram

• Division: To convert grams to kilograms, divide by 1,000

• Decimal Notation: Express results in decimal form when needed

2 Basic Conversion: Kilograms to Grams
Exercise 2
A watermelon weighs 3.2 kilograms. How many grams does it weigh?
Definition:

Conversion from Kilograms to Grams: Since 1 kilogram equals 1,000 grams, multiply by 1,000 to convert.

Step 1: Identify the number of kilograms

Weight of watermelon = 3.2 kilograms

Step 2: Apply the conversion formula

Grams = Kilograms × 1,000
Grams = 3.2 × 1,000 = 3,200

Step 3: State the result

3.2 kilograms = 3,200 grams

The watermelon weighs 3,200 g
Final answer:

The watermelon weighs 3,200 grams.

Applied rules:

• Conversion Factor: 1 kilogram = 1,000 grams

• Multiplication: To convert kilograms to grams, multiply by 1,000

• Decimal Multiplication: Move decimal point 3 places to the right

3 Comparing Weights
Exercise 3
Which is heavier: a 1.5 kg bag of flour or a 1,200 g bag of sugar? Show your work.
Definition:

Comparing Weights: To compare weights in different units, convert both to the same unit before comparing.

Step 1: Convert both weights to the same unit

Flour: 1.5 kg = 1.5 × 1,000 = 1,500 grams
Sugar: 1,200 grams

Step 2: Compare the weights

Flour: 1,500 grams
Sugar: 1,200 grams
1,500 > 1,200

Step 3: State the comparison

The bag of flour is heavier than the bag of sugar

The 1.5 kg bag of flour is heavier
Final answer:

The 1.5 kg bag of flour (1,500 g) is heavier than the 1,200 g bag of sugar.

Applied rules:

• Unit Standardization: Convert to the same unit before comparing

• Conversion: Use multiplication or division by 1,000 as needed

• Comparison: Compare numerical values once units are the same

Grams and Kilograms Rules and Methods
1,000 g = 1 kg
Conversion Formula
Grams to Kilograms
÷ 1,000
Divide by 1,000
Kilograms to Grams
× 1,000
Multiply by 1,000
Comparison
Same Unit Required
Convert first
Key Definitions:

Gram (g): A small unit of weight. Used for light objects like paper clips, coins, etc.

Kilogram (kg): A larger unit of weight. Used for heavier objects like bags, people, etc.

Conversion: Changing from one unit of measurement to another while keeping the same weight.

Basic Rule: 1,000 grams = 1 kilogram
Conversion: To go from grams to kilograms, divide by 1,000
Conversion: To go from kilograms to grams, multiply by 1,000
Tip 1: Remember: "kilo" means thousand, so 1 kilogram = 1,000 grams
Tip 2: Use a scale to practice measuring everyday objects
Tip 3: When comparing weights, always convert to the same unit first
Solution: Exercises 4 to 5
4 Adding Weights
Exercise 4
Sarah bought 2.5 kg of apples and 800 g of oranges. What is the total weight of the fruits in grams?
Definition:

Adding Weights: To add weights in different units, convert all to the same unit before adding.

Step 1: Convert all weights to the same unit

Apples: 2.5 kg = 2.5 × 1,000 = 2,500 grams
Oranges: 800 grams (already in grams)

Step 2: Add the weights together

Total weight = 2,500 grams + 800 grams = 3,300 grams

Step 3: Verify the calculation

2,500 + 800 = 3,300 ✓

Step 4: State the result

Total weight = 3,300 grams

Total weight: 3,300 g
Final answer:

The total weight of the fruits is 3,300 grams.

Applied rules:

• Unit Standardization: Convert all measurements to the same unit

• Conversion: Use multiplication by 1,000 to convert kg to g

• Addition: Add the numerical values after conversion

5 Word Problem: Sharing Weight
Exercise 5
A box of cookies weighs 1.2 kg. If the cookies are shared equally among 4 children, how many grams of cookies does each child get?
Definition:

Weight Division: Dividing a total weight by the number of people or portions to find individual shares.

Step 1: Convert the total weight to grams

1.2 kg = 1.2 × 1,000 = 1,200 grams

Step 2: Divide the total weight by the number of children

Each child gets = 1,200 grams ÷ 4 children = 300 grams per child

Step 3: Verify the calculation

300 × 4 = 1,200 ✓

Step 4: State the result

Each child gets 300 grams of cookies

Each child gets 300 g
Final answer:

Each child gets 300 grams of cookies.

Applied rules:

• Conversion: Change kilograms to grams before dividing

• Division: Divide total weight by number of people

• Equal Sharing: Each person gets the same portion

Key Concepts: Grams and Kilograms, Definitions, Methods, and Formulas
1,000 g = 1 kg
Conversion Formula
Key definitions:

Gram (g): A metric unit of weight equal to 1/1,000 of a kilogram. Used for light objects.

Kilogram (kg): The base unit of weight in the metric system. Used for heavier objects.

Weight: The measure of how heavy something is.

Complete methodology:
  1. Identify units: Determine if measurements are in grams or kilograms
  2. Convert if necessary: Change all measurements to the same unit
  3. Perform operation: Add, subtract, multiply, or divide as needed
  4. State answer: Express the result in the required unit
Tip 1: Remember: "kilo" means thousand, so 1 kilogram = 1,000 grams
Tip 2: When converting from kg to g, move the decimal point 3 places to the right
Tip 3: When converting from g to kg, move the decimal point 3 places to the left
Tip 4: Always convert to the same unit before comparing or calculating
Common errors: Forgetting to convert units, multiplying instead of dividing (or vice versa), misplacing decimal points.
Practice activities: Weigh everyday objects, practice conversions, compare weights of different items.
Formulas to know by heart:

• Conversion Formula: 1,000 grams = 1 kilogram

• Grams to Kilograms: Divide by 1,000

• Kilograms to Grams: Multiply by 1,000

• Unit Comparison: Convert to same unit before comparing

Exercise with Visualization: Common Object Weights
Exercise 6: Understanding Weight Scale
Common household items and their weights:
Paperclip: 1 gram
Apple: 150 grams
Loaf of bread: 0.5 kg
Bag of flour: 2 kg
Water bottle: 500 g
Which items weigh more than 1 kg? Convert all to grams for comparison.

Analysis: Convert all weights to grams and compare to 1,000 grams (1 kg).

  • Paperclip: 1 gram
  • Apple: 150 grams
  • Loaf of bread: 0.5 kg = 500 grams
  • Bag of flour: 2 kg = 2,000 grams
  • Water bottle: 500 grams
  • Items weighing more than 1 kg (1,000 g): Only the bag of flour (2,000 g)

Questions & Answers

Question: My 3rd grade students often confuse grams and kilograms. How can I help them understand the difference?

Answer: Here are effective strategies for teaching the difference between grams and kilograms:

  • Concrete examples: Use real objects - a paperclip weighs about 1 gram, a textbook weighs about 1 kilogram
  • Size comparison: Emphasize that 1,000 grams equal 1 kilogram
  • Hands-on activities: Let students hold objects of different weights

Examples:

  • Light objects (grams): paperclip, coin, small apple
  • Heavier objects (kilograms): textbook, bag of sugar, child's backpack

Create a classroom weight station with labeled objects for hands-on learning.

Question: My child gets confused when converting between grams and kilograms. What strategies can help them?

Answer: Effective strategies for gram/kilogram conversion:

  • Memory trick: "kilo" means thousand, so 1 kilogram = 1,000 grams
  • Direction matters: Grams to kilograms = divide by 1,000; Kilograms to grams = multiply by 1,000
  • Decimal movement: Moving decimal 3 places left (÷) or right (×)

Practice examples:

  • To convert 2,500 g to kg: 2,500 ÷ 1,000 = 2.5 kg
  • To convert 3.2 kg to g: 3.2 × 1,000 = 3,200 g

Practice with kitchen scales to make the concept more tangible.

Question: How do I know when to multiply and when to divide when converting?

Answer: Think about which unit is bigger:

  • Kilograms are bigger than grams
  • Going from big to small (kg to g): MULTIPLY by 1,000
  • Going from small to big (g to kg): DIVIDE by 1,000

Examples:

  • 3 kg to grams: 3 × 1,000 = 3,000 g (multiply because going from big to small)
  • 5,000 g to kg: 5,000 ÷ 1,000 = 5 kg (divide because going from small to big)

Remember: More grams equal fewer kilograms because grams are smaller units!

Question: What if I have decimals when converting? Like 2.5 kg to grams?

Answer: When working with decimals, the same rules apply:

  • For kg to g: Multiply by 1,000 (move decimal point 3 places to the right)
  • For g to kg: Divide by 1,000 (move decimal point 3 places to the left)

For 2.5 kg to grams:

  • 2.5 × 1,000 = 2,500 grams
  • You can think: 2.5 → 25.0 → 250.0 → 2,500.0
  • Move the decimal point 3 places to the right

More examples:

  • 0.75 kg = 750 g (0.750 → 750)
  • 1,250 g = 1.25 kg (1250. → 1.250)

Question: How do I check if my answer is right? Sometimes I'm not sure about my conversions.

Answer: Here are effective ways to check your conversions:

  • Reverse calculation: Convert back to the original unit to see if you get the starting value
  • Reasonableness check: Does your answer make sense? (Fewer kg should equal more g)
  • Factor of 1,000: Check if the numbers differ by a factor of 1,000

Example: If you convert 2.5 kg to 2,500 g:

  • Reverse: 2,500 g ÷ 1,000 = 2.5 kg ✓
  • Reasonable: 2.5 kg is less than 2,500 g ✓
  • Factor: 2,500 ÷ 2.5 = 1,000 ✓

Always double-check by using the reverse operation!