Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Mass tells us how heavy or light an object is. In a balance scale (a tool with two pans), the side with the heavier object moves downwards, while the side with the lighter object moves upwards. If both pans are at the same level, the weights are equal.
Standard Units: To measure weight accurately, we use standard units called Grams and Kilograms. Using standard units ensures that the weight of an object is the same no matter who weighs it or where it is weighed.
Gram (): This is a smaller unit used to measure light objects. For example, a pencil, a chocolate bar, or an eraser are measured in grams. A visual reference for is the weight of a single small paperclip.
Kilogram (): This is a larger unit used to measure heavy objects. For example, a bag of wheat, a watermelon, or a bicycle are measured in kilograms. A weight is roughly equal to the weight of a -liter bottle of water.
Relationship between Units: The connection between the two units is that kilogram is made up of grams. This can be visualized as placing a block on one side of a scale and needing tiny weights on the other side to balance it perfectly: .
Common Weights: Shopkeepers use metal weights of different sizes like and . By combining these on a beam balance, they can weigh any amount of vegetables or fruits accurately.
Comparing Weights: To compare two weights, we look at both the number and the unit. Even if the number is small, a kilogram unit makes it much heavier than a gram unit (e.g., is heavier than ). If units are the same, the higher number is heavier ( is heavier than ).
📐Formulae
💡Examples
Problem 1:
Convert into grams.
Solution:
Step 1: Convert the kilograms into grams. Since , then . \nStep 2: Add the remaining grams to the converted amount: .
Explanation:
To find the total weight in grams, we first change the part to by multiplying by and then add the existing portion.
Problem 2:
A packet of sugar weighs and a packet of flour weighs . Which one is heavier?
Solution:
Step 1: Convert the sugar weight into grams to compare: . \nStep 2: Compare the two values: (Sugar) and (Flour). \nStep 3: Since , the sugar packet is heavier.
Explanation:
To compare two weights with different units, convert them both to the same unit (grams). Comparing and shows that the packet has more mass.