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Measurement - Measurement of Length using Metric Units

Grade 3ICSE

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

🔑Concepts

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Definition of Length: Length measures how long an object is or the distance between two points. To visualize this, imagine placing a wooden ruler alongside a pencil; the distance from the beginning of the pencil to its tip is its length.

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Standard Units of Measurement: In the metric system, we use different units based on size. For small objects like a notebook, we use centimetres (cmcm). For medium objects like the height of a wall, we use metres (mm). For long distances like the road between two cities, we use kilometres (kmkm). Imagine a small paperclip as 1 cm1\text{ cm} and a large adult step as 1 m1\text{ m}.

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Measuring with a Ruler: When using a ruler, always start measuring from the '00' mark, not the physical edge of the ruler. If you look closely at a 15 cm15\text{ cm} ruler, you will see 1010 small marks between each centimetre; these represent millimetres.

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The Metre (mm): The metre is the standard unit of length. One metre is made up of exactly 100 centimetres100\text{ centimetres}. Think of a metre rod used by a tailor; it is much longer than your school ruler and is used to measure cloth.

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The Kilometre (kmkm): This unit is used for very long distances. One kilometre is equal to 1000 metres1000\text{ metres}. To visualize this distance, imagine walking the length of a standard football field 1010 times.

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Conversion Rules: To convert a larger unit to a smaller unit, we multiply. For example, to change metres to centimetres, we multiply the number of metres by 100100. To change kilometres to metres, we multiply the number of kilometres by 10001000.

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Addition and Subtraction of Length: When adding or subtracting lengths, we group the same units together. It is helpful to visualize two columns—one for 'mm' and one for 'cmcm'. Always solve the 'cmcm' column first. If the sum of the centimetres is 100100 or more, we carry over to the metres column.

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Real-world Visuals: A finger's width is approximately 1 cm1\text{ cm}, the width of a single door is about 1 m1\text{ m}, and a 1515-minute walk covers roughly 1 km1\text{ km}.

📐Formulae

1 m=100 cm1\text{ m} = 100\text{ cm}

1 km=1000 m1\text{ km} = 1000\text{ m}

Length in cm=Length in m×100\text{Length in cm} = \text{Length in m} \times 100

Length in m=Length in km×1000\text{Length in m} = \text{Length in km} \times 1000

💡Examples

Problem 1:

Convert 8 m 45 cm8\text{ m } 45\text{ cm} into centimetres.

Solution:

Step 1: Convert the metres into centimetres using the formula 1 m=100 cm1\text{ m} = 100\text{ cm}. 8 m=8×100=800 cm8\text{ m} = 8 \times 100 = 800\text{ cm} Step 2: Add the remaining centimetres to the result. 800 cm+45 cm=845 cm800\text{ cm} + 45\text{ cm} = 845\text{ cm} Final Answer: 845 cm845\text{ cm}

Explanation:

To convert a mixed measurement of metres and centimetres into only centimetres, we first change the metres by multiplying by 100100 and then add the extra centimetres.

Problem 2:

Add 15 m 65 cm15\text{ m } 65\text{ cm} and 12 m 50 cm12\text{ m } 50\text{ cm}.

Solution:

Step 1: Set up columns for mm and cmcm. Add the cmcm column first: 65+50=115 cm65 + 50 = 115\text{ cm}. Step 2: Since 115 cm115\text{ cm} is 100 cm+15 cm100\text{ cm} + 15\text{ cm}, it equals 1 m 15 cm1\text{ m } 15\text{ cm}. Step 3: Write 1515 in the cmcm column and carry over the 1 m1\text{ m} to the mm column. Step 4: Add the mm column: 15+12+1 (carried)=28 m15 + 12 + 1\text{ (carried)} = 28\text{ m}. Result: 28 m 15 cm28\text{ m } 15\text{ cm}

Explanation:

When adding lengths, if the centimetre sum exceeds 100100, we must convert that 100 cm100\text{ cm} into 1 m1\text{ m} and carry it over to the metres column, just like regrouping in basic addition.