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Measurement - Measurement of Weight using Metric Units

Grade 3ICSE

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' (gg): The gram is the standard metric unit used to measure the weight of light objects. For example, a single paperclip weighs about 1 g1\ g, and a pencil weighs about 5 g5\ g. Think of a few drops of water in your palm to visualize the weight of 1 g1\ g.

The Unit 'Kilogram' (kgkg): 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 1 kg1\ kg. Visualize holding a large bag of sugar to understand how 1 kg1\ kg feels.

Conversion Rule: There is a fixed relationship between the two units: 10001000 grams make up 11 kilogram. This is written as 1 kg=1000 g1\ kg = 1000\ g. This means a kilogram is 10001000 times heavier than a gram.

Converting kgkg to gg: To change kilograms into grams, we multiply the number of kilograms by 10001000. For example, 4 kg4\ kg becomes 4×1000=4000 g4 \times 1000 = 4000\ g. 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 2 kg 500 g2\ kg\ 500\ g), we convert the kilogram part to grams first and then add the remaining grams. For example, 2 kg 500 g=2000 g+500 g=2500 g2\ kg\ 500\ g = 2000\ g + 500\ g = 2500\ g.

Standard Weights: In shops, you might see metal weights used on balance scales. These typically come in denominations like 50 g,100 g,200 g,500 g,1 kg,2 kg,50\ g, 100\ g, 200\ g, 500\ g, 1\ kg, 2\ kg, and 5 kg5\ kg. To weigh an object of 750 g750\ g, a shopkeeper might use a 500 g500\ g weight and a 200 g200\ g weight and a 50 g50\ g weight together.

Comparison of Weights: To compare two weights, they should be in the same unit. Since 1 kg=1000 g1\ kg = 1000\ g, a 900 g900\ g box is lighter than a 1 kg1\ kg box, even though 900900 is a larger number than 11.

📐Formulae

1 kg=1000 g1\ kg = 1000\ g

1000 g=1 kg1000\ g = 1\ kg

Weight in grams=(Weight in kg×1000)+extra grams\text{Weight in grams} = (\text{Weight in } kg \times 1000) + \text{extra grams}

12 kg=500 g\frac{1}{2}\ kg = 500\ g

💡Examples

Problem 1:

Convert 5 kg 45 g5\ kg\ 45\ g into grams.

Solution:

Step 1: Use the formula 1 kg=1000 g1\ kg = 1000\ g. \ Step 2: Convert the kilogram part: 5 kg=5×1000=5000 g5\ kg = 5 \times 1000 = 5000\ g. \ Step 3: Add the remaining grams: 5000 g+45 g=5045 g5000\ g + 45\ g = 5045\ g. \ Final Answer: 5045 g5045\ g.

Explanation:

To convert to grams, we first change the kilograms into grams by multiplying by 10001000 and then add the additional gram value given in the problem.

Problem 2:

A fruit seller sold 3 kg 250 g3\ kg\ 250\ g of apples and 4 kg 500 g4\ kg\ 500\ g of mangoes. What is the total weight of the fruits sold?

Solution:

Step 1: Create two columns for kgkg and gg. \ Step 2: Write the weights: \ kgkg column: 33 and 44 \ gg column: 250250 and 500500 \ Step 3: Add the grams: 250 g+500 g=750 g250\ g + 500\ g = 750\ g. \ Step 4: Add the kilograms: 3 kg+4 kg=7 kg3\ kg + 4\ kg = 7\ kg. \ Total weight = 7 kg 750 g7\ kg\ 750\ g.

Explanation:

We add the weights by grouping the grams together and the kilograms together. Since the sum of grams (750750) is less than 10001000, no carry-over to the kilogram column is needed.