Measuring Length Revision Notes for Grade 12 NSC Matric Mathematical Literacy

Measuring Length

Understanding estimation in measurement

Estimation is a valuable technique used to find approximate values for measurements without using precise measuring tools. This skill is particularly useful in everyday situations where you need quick measurements or want to check if your precise measurements are reasonable.

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Estimation serves two main purposes in measurement:

Providing quick approximations when precise tools aren't available
Acting as a "reality check" to verify that your precise measurements are sensible

Common estimation references

When estimating length, you can use familiar body measurements and everyday objects as reference points:

One metre is approximately the distance from your shoulder to your fingertips when you stand with your arm outstretched
One metre is also roughly the distance of one large step or jump
These references help you quickly estimate distances and lengths in practical situations

Practical measurement problems

Material and cost calculations

When working with materials that are sold by length, you need to calculate both the quantity required and the total cost.

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Basic Cost Formula:

$\text{Total Cost} = \text{Length of Material} \times \text{Price per Metre}$

This fundamental formula applies to all material purchasing problems.

However, real-world problems often involve multiple requirements and practical considerations such as:

Materials sold only in full metre lengths
Multiple items requiring different amounts
Additional materials (like cotton for embroidery)

Worked examples

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Worked Example 1: Window Curtain Material

Carl needs to measure a window width to buy curtain material. The material costs R55 per metre and is sold only in full metres.

Problem setup:

Carl estimates the window width as 1.9 metres using his arm measurement
Later, he measures accurately and finds the window is actually 2.2 metres wide

Step-by-step solution:

Part A: Using the estimate (1.9 metres)

Material needed: Since material is sold in full metres only, Carl needs 2 metres
Cost calculation: $2 \times \text{R}55 = \text{R}110$

Part B: Using accurate measurement (2.2 metres)

Material needed: Since material is sold in full metres only, Carl needs 3 metres
Cost calculation: $3 \times \text{R}55 = \text{R}165$

Key insight: Accurate measurement showed Carl needed 1 metre more material, costing R55 extra.

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Worked Example 2: Dress-making Materials

Liz sews children's dresses with different material requirements and additional embroidery cotton.

Given information:

Main material costs R89.50 per metre
Material needed: 2.5m (7-year-old), 2m (4-year-old), 2m (4-year-old), 3m (10-year-old)
Embroidery cotton costs R12.55 per roll of 3 metres
Uses 2 rolls of cotton per dress

Step-by-step calculations:

Step 1: Total material needed

$2.5\text{m} + 2\text{m} + 2\text{m} + 3\text{m} = 9.5\text{m}$

Step 2: Material cost

$\text{Length} \times \text{Price} = 9.5\text{m} \times \text{R}89.50 = \text{R}850.25$

Step 3: Cotton per dress

$\text{Length of one roll} \times 2 = 3\text{m} \times 2 = 6\text{m} \text{ (or 600cm) per dress}$

Step 4: Total cotton cost

$\text{Number of dresses} \times 2 \text{ rolls per dress} \times \text{price per roll}$

$= 4 \times 2 \times \text{R}12.55 = \text{R}100.40$

Step 5: Total cost for 10-year-old dress

$\text{Material cost} + \text{Cotton cost} = (3\text{m} \times \text{R}89.50) + (2 \times \text{R}12.55)$

$= \text{R}268.50 + \text{R}25.10 = \text{R}293.60$

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Worked Example 3: Table Decoration Project

Jenny decorates rectangular tables (3m × 1m) with tablecloths that must hang 20cm over all edges.

Problem analysis:

Table dimensions: 3m length × 1m width
Overhang required: 20cm on all sides
Fabric costs R75 per metre, sold in lengths smaller than 1 metre
Fabric width: 1.4m

Step-by-step solution:

Step 1: Calculate total cloth dimensions

Length needed: $3\text{m} + 0.2\text{m} + 0.2\text{m} = 3.4\text{m}$
Width needed: $1\text{m} + 0.2\text{m} + 0.2\text{m} = 1.4\text{m}$

Step 2: Cost per table $\text{Length} \times \text{Price} = 3.4\text{m} \times \text{R}75 = \text{R}255.00$

Step 3: Total cost for 15 tables $15 \text{ tables} \times \text{R}255.00 = \text{R}3,825.00$

Key measurement principles

Unit conversion reminders

Understanding unit relationships is crucial for accurate calculations:

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Essential Conversions:

$1 \text{ metre} = 100 \text{ centimetres}$
Always check what units are required in your final answer
Convert between units carefully in multi-step problems

Problem-solving approach

Follow this systematic approach to tackle measurement problems effectively:

Read carefully - identify what is being asked
List known information - dimensions, prices, quantities
Plan your calculation - break complex problems into steps
Check reasonableness - do your answers make sense?
Include units - always specify metres, centimetres, or currency

Common exam considerations

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Critical Points to Remember:

Materials often sold in full units only (round up when necessary)
Multiple calculations may be needed for complex problems
Cost calculations typically involve multiplication of length and price
Estimation can help check if precise answers are reasonable

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Key Points to Remember:

One metre equals the distance from shoulder to fingertips or one large step
Estimation helps you quickly assess measurements and check precise calculations
Always round up when materials are sold in full units only
Total cost = Length of material × Price per unit
Complex problems often require multiple calculation steps - break them down systematically

Measuring Length (Grade 12 NSC Matric Mathematical Literacy): Revision Notes