Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Understanding Mass and Weight: Weight (or mass) tells us how heavy an object is. In Grade 3, we use weighing balances and digital scales to measure weight. Imagine a balance scale with two pans: if one pan is lower than the other, the object in that pan is heavier. If the pans are level, the weights are equal.
The Unit 'Gram' (): The gram is the standard metric unit used to measure the weight of light objects. For example, a single paperclip weighs about , and a pencil weighs about . Think of a few drops of water in your palm to visualize the weight of .
The Unit 'Kilogram' (): The kilogram is the standard metric unit used to measure the weight of heavy objects. For example, a large textbook or a liter of water weighs approximately . Visualize holding a large bag of sugar to understand how feels.
Conversion Rule: There is a fixed relationship between the two units: grams make up kilogram. This is written as . This means a kilogram is times heavier than a gram.
Converting to : To change kilograms into grams, we multiply the number of kilograms by . For example, becomes . A quick way to visualize this is adding three zeros to the end of the kilogram value.
Converting Mixed Units: When we have both kilograms and grams (like ), we convert the kilogram part to grams first and then add the remaining grams. For example, .
Standard Weights: In shops, you might see metal weights used on balance scales. These typically come in denominations like and . To weigh an object of , a shopkeeper might use a weight and a weight and a weight together.
Comparison of Weights: To compare two weights, they should be in the same unit. Since , a box is lighter than a box, even though is a larger number than .
📐Formulae
💡Examples
Problem 1:
Convert into grams.
Solution:
Step 1: Use the formula . \ Step 2: Convert the kilogram part: . \ Step 3: Add the remaining grams: . \ Final Answer: .
Explanation:
To convert to grams, we first change the kilograms into grams by multiplying by and then add the additional gram value given in the problem.
Problem 2:
A fruit seller sold of apples and of mangoes. What is the total weight of the fruits sold?
Solution:
Step 1: Create two columns for and . \ Step 2: Write the weights: \ column: and \ column: and \ Step 3: Add the grams: . \ Step 4: Add the kilograms: . \ Total weight = .
Explanation:
We add the weights by grouping the grams together and the kilograms together. Since the sum of grams () is less than , no carry-over to the kilogram column is needed.