Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Understanding Weight: Weight measures how heavy an object is. In our daily lives, we use different units to measure weight based on the size of the object. We use grams () for light objects and kilograms () for heavy ones. Visualise a single toffee or a paperclip; these are measured in grams. Visualise a large watermelon or your own body; these are measured in kilograms.
The Gram (): The gram is a small unit of weight. If you hold a single dry bean or a small button, you are feeling a weight of approximately . Grams are used for things like spices, jewellery, and small stationery items.
The Kilogram (): The kilogram is the standard unit for heavier items. Imagine a bottle of water; it weighs about . We buy vegetables like potatoes or staples like rice in kilograms.
The Relationship Between Units: The most important rule to remember is that grams make up kilogram (). If you have a balance scale with a weight on one side, you would need tiny weights on the other side to keep it perfectly level.
Using a Balance Scale: A balance scale or beam balance is used to compare weights. It consists of two pans hanging from a central bar. Visualise the scale: if the left pan is lower than the right pan, it means the object on the left is 'heavier'. If both pans are at the exact same height, the weights are 'equal'.
Standard Weights: To measure accurately, we use fixed weights made of metal. These usually come in denominations such as and . Shops often use these on manual scales to weigh flour or sugar.
Converting Units: To change kilograms into grams, we multiply by because is a larger unit. To change grams into kilograms, we divide by . For example, half a kilogram is represented as , which is exactly because .
📐Formulae
💡Examples
Problem 1:
Convert into grams.
Solution:
Step 1: We know that . \nStep 2: Convert the part to by multiplying: . \nStep 3: Add the remaining grams: . \nTotal = .
Explanation:
To convert a mixed unit (kg and g) into grams, first transform the kilograms into grams and then add the extra grams to get the total.
Problem 2:
Rahul bought of potatoes and of onions. What is the total weight of the vegetables in kilograms and grams?
Solution:
Step 1: Add the grams: . \nStep 2: Since is more than , we split it: . \nStep 3: Add the kilograms: . \nStep 4: Combine the results: .
Explanation:
When adding weights, add the grams first. If the grams exceed , convert to and carry it over to the kilogram column.