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Measurement - Measurement of Weight

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Weight, often called Mass in mathematics, measures how heavy an object is. In the ICSE Grade 4 curriculum, we focus on three main units: Milligrams (mgmg), Grams (gg), and Kilograms (kgkg). Imagine a tiny grain of salt weighing a few mgmg, a single grape weighing about 55 gg, and a large pumpkin weighing 55 kgkg.

The Kilogram (kgkg) is the standard unit of weight used for heavier objects like suitcases, human body weight, or sacks of flour. A common visual for 11 kgkg is a standard liter bottle of water or a large bag of sugar.

The Gram (gg) is used for lighter objects. You can visualize 11 gg as the weight of a small metal paperclip or a single plastic pen cap. There are exactly 10001000 grams in one kilogram, which makes the gram a 'sub-multiple' of the kilogram.

The Milligram (mgmg) is the smallest unit we study, used for very light items like feathers, flower petals, or the dosage of medicine in a tablet. Visually, 10001000 milligrams are packed into just 11 single gram.

To convert from a larger unit to a smaller unit, we use multiplication. When moving 'down' the unit scale from kgkg to gg, we multiply by 10001000. For example, 22 kgkg becomes 2×1000=20002 \times 1000 = 2000 gg. You can visualize this as 'expanding' the number as you move to a smaller, more precise unit.

To convert from a smaller unit to a larger unit, we use division. When moving 'up' the scale from gg to kgkg, we divide the value by 10001000. For instance, 50005000 gg becomes 5000÷1000=55000 \div 1000 = 5 kgkg. If a number is not a perfect multiple of 10001000, the remainder stays in the smaller unit (e.g., 45004500 gg is 44 kgkg and 500500 gg).

We use different types of balances to measure weight. A manual Beam Balance uses two pans; one pan holds the object and the other holds standard metal weights. When the horizontal beam is perfectly straight, the weights are equal. Modern Electronic Balances show the weight as a digital number on a screen for higher precision.

📐Formulae

1 kilogram (kg)=1000 grams (g)1\text{ kilogram (kg)} = 1000\text{ grams (g)}

1 gram (g)=1000 milligrams (mg)1\text{ gram (g)} = 1000\text{ milligrams (mg)}

Weight in grams=Weight in kg×1000\text{Weight in grams} = \text{Weight in kg} \times 1000

Weight in kilograms=Weight in grams1000\text{Weight in kilograms} = \frac{\text{Weight in grams}}{1000}

Total Weight=Weight of Container+Weight of Contents\text{Total Weight} = \text{Weight of Container} + \text{Weight of Contents}

💡Examples

Problem 1:

Convert 8 kg 425 g8\text{ kg } 425\text{ g} into grams.

Solution:

Step 1: Identify the relationship between kgkg and gg. We know that 1 kg=1000 g1\text{ kg} = 1000\text{ g}. \ Step 2: Convert the 8 kg8\text{ kg} portion into grams: 8×1000=8000 g8 \times 1000 = 8000\text{ g}. \ Step 3: Add the remaining grams to the converted amount: 8000 g+425 g=8425 g8000\text{ g} + 425\text{ g} = 8425\text{ g}. \ Final Answer: 8425 g8425\text{ g}.

Explanation:

To convert a mixed unit (kg and g) into a single smaller unit (g), we first change the kilograms into grams by multiplying by 1000 and then add the extra grams.

Problem 2:

Subtract 5 kg 750 g5\text{ kg } 750\text{ g} from 12 kg 250 g12\text{ kg } 250\text{ g}.

Solution:

Step 1: Arrange the values in two columns: kgkg and gg. \  kg | g  12 | 250 - 05 | 750————-Step2:Sincewecannotsubtract\text{ kg | g }\\ \text{ 12 | 250}\\ \text{ - 05 | 750}\\ \text{-------------}\\ Step 2: Since we cannot subtract 750fromfrom250,borrow, borrow 1\text{ kg}fromthefrom thekgcolumn.column. \\12\text{ kg}becomesbecomes11\text{ kg}.Theborrowed. \\ The borrowed 1\text{ kg}isis1000\text{ g}.Addthisto. Add this to 250\text{ g}togetto get1250\text{ g}.Step3:Subtractthegrams:. \\ Step 3: Subtract the grams: 1250\text{ g} - 750\text{ g} = 500\text{ g}.Step4:Subtractthekilograms:. \\ Step 4: Subtract the kilograms: 11\text{ kg} - 5\text{ kg} = 6\text{ kg}.FinalAnswer:. \\ Final Answer: 6\text{ kg } 500\text{ g}$.

Explanation:

When subtracting weight, if the grams in the top number are less than the grams in the bottom number, we borrow 11 kgkg (10001000 gg) from the kilogram column to make the subtraction possible.