Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Weight is a measure of how heavy or light an object is. We use a balance scale to compare weights; visually, the pan with the heavier object moves downwards, while the pan with the lighter object moves upwards. If the two pans are perfectly level, the weights are equal.
The standard units for measuring weight are grams () and kilograms (). Grams are used for light objects like a pencil, a spoon, or an eraser. Kilograms are used for heavier objects like a school bag, a watermelon, or a bag of rice.
The relationship between the two units is that is equal to . You can visualize as being made up of small weights grouped together.
To convert kilograms () into grams (), we multiply the number of kilograms by . For example, to find the grams in , we calculate .
To convert grams () into kilograms (), we divide the number of grams by . For example, is equal to .
Shopkeepers use standard metal weights to measure items on a balance. These weights usually come in sizes like , , , , , , and . To measure an object weighing , a shopkeeper might place a , a , and a weight together in one pan.
When dealing with mixed units like , we convert the kilogram part to grams first () and then add the remaining grams () to get a total of .
📐Formulae
💡Examples
Problem 1:
Convert into grams.
Solution:
Step 1: Convert to grams: . \ Step 2: Add the remaining grams: . \ Final Answer:
Explanation:
Since , we multiply the kilograms by and then add the extra grams to find the total.
Problem 2:
Convert into kilograms.
Solution:
Step 1: Use the conversion formula . \ Step 2: Divide by : . \ Final Answer:
Explanation:
To change a smaller unit (grams) to a larger unit (kilograms), we divide the value by .