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Measurement - Measurement of Length

Grade 4ICSE

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

🔑Concepts

Standard Units of Length: Length is the distance between two points. In the ICSE Grade 4 curriculum, we primarily use Kilometres (kmkm) for long distances like between cities, Metres (mm) for heights of buildings or lengths of cloth, and Centimetres (cmcm) or Millimetres (mmmm) for small objects like pencils or notebooks. Imagine a long highway stretching out for kmkm and a small wooden ruler for cmcm.

Measuring with a Ruler: A standard 15cm15 cm ruler is used for measuring small objects. Each centimetre is divided into 1010 equal parts called millimetres. When measuring, you must always align the '0' mark of the ruler with the start of the object. Visualize the edge of your pencil tip starting exactly at the 00 line and ending at a specific number on the ruler.

The Base Unit (Metre): The Metre (mm) is the standard unit of length. One metre is approximately the distance from the floor to the waist of an average adult, or the width of a standard doorway. It takes 100100 centimetre markings on a measuring tape to make exactly 11 metre.

Conversion of Units (Big to Small): To change a larger unit to a smaller unit, we always multiply. For example, since 1m=100cm1 m = 100 cm, to convert 5m5 m to cmcm, you multiply 55 by 100100. Think of this as breaking down a large block into many smaller pieces; the number of pieces increases.

Conversion of Units (Small to Big): To change a smaller unit to a larger unit, we divide. For example, to convert 2000m2000 m to kmkm, you divide 20002000 by 10001000. Visualize gathering 10001000 individual 11-metre sticks and bundling them together to create a single 11 kilometre block.

Addition and Subtraction of Length: When performing operations, always align the units in separate columns (e.g., a column for mm and a column for cmcm). If the sum in the cmcm column reaches 100100 or more, you must carry over to the mm column because 100cm=1m100 cm = 1 m.

Understanding Kilometres: Kilometres are used for measuring very long distances. 1km1 km is equal to 1000m1000 m. If you imagine a standard running track, which is usually 400m400 m long, two and a half laps around that track would roughly equal 1km1 km.

📐Formulae

1 kilometre (km)=1000 metres (m)1 \text{ kilometre (km)} = 1000 \text{ metres (m)}

1 metre (m)=100 centimetres (cm)1 \text{ metre (m)} = 100 \text{ centimetres (cm)}

1 centimetre (cm)=10 millimetres (mm)1 \text{ centimetre (cm)} = 10 \text{ millimetres (mm)}

To convert km to m=Value in km×1000\text{To convert km to m} = \text{Value in km} \times 1000

To convert m to cm=Value in m×100\text{To convert m to cm} = \text{Value in m} \times 100

To convert cm to m=Value in cm÷100\text{To convert cm to m} = \text{Value in cm} \div 100

💡Examples

Problem 1:

Convert 7m25cm7 m 25 cm into centimetres.

Solution:

Step 1: Convert the metres into centimetres. We know that 1m=100cm1 m = 100 cm. So, 7m=7×100=700cm7 m = 7 \times 100 = 700 cm. \ Step 2: Add the remaining centimetres to the result. Total =700cm+25cm=725cm= 700 cm + 25 cm = 725 cm.

Explanation:

To convert a length given in mixed units (metres and centimetres) into a single unit (centimetres), first transform the larger unit by multiplying by its conversion factor (100100) and then add the smaller units.

Problem 2:

Add 24m85cm24 m 85 cm and 15m40cm15 m 40 cm.

Solution:

Step 1: Add the centimetres: 85cm+40cm=125cm85 cm + 40 cm = 125 cm. \ Step 2: Convert 125cm125 cm to metres and centimetres: 125cm=1m25cm125 cm = 1 m 25 cm. \ Step 3: Keep 25cm25 cm in the centimetre column and carry over 1m1 m to the metre column. \ Step 4: Add the metres: 24m+15m+1m (carry)=40m24 m + 15 m + 1 m \text{ (carry)} = 40 m. \ Final Answer: 40m25cm40 m 25 cm.

Explanation:

When adding lengths, treat the centimetres separately. If they exceed 100100, convert every 100cm100 cm into 1m1 m and carry it over to the metres column, just like regular addition with carry-over.