Measuring Mass or Weight Revision Notes for Grade 12 NSC Matric Mathematical Literacy

Measuring Mass or Weight

Understanding mass and weight terminology

Mass is the scientific term used to describe how much an object weighs when measured on a scale. However, in everyday language, we often use the words "weight" and "mass" interchangeably, and both terms are acceptable for practical calculations.

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For mathematical literacy purposes, you can treat these terms as meaning the same thing - they both refer to how heavy something is. The scientific distinction between mass and weight is not critical for these practical calculations.

Essential unit conversions

Understanding how to convert between different units of weight is crucial for solving problems effectively.

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Key conversion factors you must memorise:

1 tonne = 1 000 kg
1 kg = 1 000 g
1 tonne = 1 000 000 g

When converting larger units to smaller units, you multiply. When converting smaller units to larger units, you divide.

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Worked Example 1: Converting tonnes to kilograms

Problem: A lift can carry 2,2 tonnes or a maximum of 20 people. What is the average weight per person that the engineer estimated?

Solution: Step 1: Convert tonnes to kilogrammes $2{,}2 \text{ tonnes} = 2{,}2 \times 1000 = 2200 \text{ kg}$

Step 2: Divide by number of people $\frac{2200 \text{ kg}}{20 \text{ people}} = 110 \text{ kg per person}$

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Worked Example 2: Complex weight calculations

Problem: A bus seats 50 passengers, each allowed 30 kg luggage. If 50 people averaging 80 kg each have luggage averaging 29 kg each:

Calculate total load in tonnes
If the bus weighs 4 tonnes, find total weight including passengers and luggage

Solution: Step 1: Calculate passenger weight $50 \times 80 \text{ kg} = 4000 \text{ kg}$

Step 2: Calculate luggage weight
$50 \times 29 \text{ kg} = 1450 \text{ kg}$

Step 3: Add passenger and luggage weights $4000 + 1450 = 5450 \text{ kg} = 5{,}45 \text{ tonnes}$

Step 4: Add bus weight for total $4 \text{ tonnes} + 5{,}45 \text{ tonnes} = 9{,}45 \text{ tonnes} = 9450 \text{ kg}$

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Worked Example 3: Converting grammes to kilograms

Problem: Sweet Jam comes in boxes containing 25 tins of 250g each. Calculate:

Weight of jam per box in kg
Total weight if ordering 15 boxes

Solution: Step 1: Calculate weight per box $25 \times 250\text{g} = 6250\text{g}$

Step 2: Convert to kilogrammes $6250\text{g} \div 1000 = 6{,}25\text{kg}$

Step 3: Calculate total for 15 boxes $15 \times 6{,}25\text{kg} = 93{,}75\text{kg}$

Percentage calculations with weight

Weight percentages often appear in safety contexts, such as determining safe carrying loads.

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Key principle for safety calculations: Safe carrying weight = Percentage × Body weight

This principle is commonly used in workplace safety, hiking guidelines, and physical therapy recommendations.

Example: You should never carry more than 15% of your body weight. For a person weighing 66 kg: $15% \times 66\text{kg} = 0{,}15 \times 66 = 9{,}9\text{kg}$

Cost calculations involving weight

Many real-world problems combine weight measurements with financial calculations. These are common in construction, manufacturing, and retail contexts.

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Method for cost calculations:

Identify the rate: Cost per unit weight (e.g., R23 per kg)
Calculate total weight needed
Multiply: Total weight × Cost per unit
Add costs if multiple items involved

Example: Sand costs R23 per kg, and you need 0,8 tonnes:

Convert: $0{,}8 \text{ tonnes} = 800\text{kg}$
Calculate cost: $800\text{kg} \times \text{R}23 = \text{R}18400$

Exam tips and common mistakes

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Critical points to avoid losing marks:

Always check units - ensure you're working in the same units throughout
Convert tonnes to kg by multiplying by 1000
Round appropriately - follow the precision given in the question
Show conversion steps clearly - examiners award marks for method
Check if your answer makes sense - a person shouldn't weigh 800kg!

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Key formulas to remember:

Tonne to kg conversion: $\text{tonnes} \times 1000 = \text{kg}$
Percentage calculation: $\frac{\text{percentage}}{100} \times \text{total amount}$
Cost calculation: $\text{quantity} \times \text{price per unit} = \text{total cost}$
Average weight: $\frac{\text{total weight}}{\text{number of items}}$

Essential points to remember:

Mass and weight can be used interchangeably in everyday calculations
1 tonne equals 1000 kg - remember the three zeros for quick conversions
Always convert to the same units before doing calculations
Percentage of body weight is often used for safety guidelines (typically 15% maximum)
Show your conversion steps clearly in exams to earn maximum marks

Measuring Mass or Weight (Grade 12 NSC Matric Mathematical Literacy): Revision Notes