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Physical Quantities and Measurement - Measurement of Length

Grade 6ICSE

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

🔑Concepts

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Length is defined as the distance between any two points in space.

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The standard SI unit of length is the metre, represented by the symbol mm.

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Multiples of the metre: For measuring large distances, we use the kilometre (kmkm), where 1 km=1000 m1 \text{ km} = 1000 \text{ m}.

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Sub-multiples of the metre: For measuring small lengths, we use the centimetre (cmcm) and millimetre (mmmm).

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Parallax Error: To get an accurate measurement, the eye must be placed vertically above the point where the measurement is being taken. Position of the eye at an angle leads to incorrect readings.

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Measuring Curved Lines: Since a ruler is straight, a curved line is measured using a thread. The thread is placed along the curve, marked, and then the straightened thread is measured against a ruler.

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Zero Error: If the zero mark of a ruler is broken or worn out, we should measure from another full mark (e.g., 1 cm1 \text{ cm}) and subtract that value from the final reading.

📐Formulae

1 km=1000 m=103 m1 \text{ km} = 1000 \text{ m} = 10^3 \text{ m}

1 m=100 cm=102 cm1 \text{ m} = 100 \text{ cm} = 10^2 \text{ cm}

1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

1 m=1000 mm=103 mm1 \text{ m} = 1000 \text{ mm} = 10^3 \text{ mm}

Actual Length=Final Reading−Initial Reading\text{Actual Length} = \text{Final Reading} - \text{Initial Reading}

💡Examples

Problem 1:

A student uses a ruler where the zero mark is broken. He starts measuring from the 2.5 cm2.5 \text{ cm} mark and the end of the object reaches the 9.8 cm9.8 \text{ cm} mark. What is the actual length of the object?

Solution:

Actual Length=9.8 cm−2.5 cm=7.3 cm\text{Actual Length} = 9.8 \text{ cm} - 2.5 \text{ cm} = 7.3 \text{ cm}

Explanation:

When the zero mark is unavailable, the actual length is the difference between the final reading and the starting point reading.

Problem 2:

Convert a distance of 4.5 km4.5 \text{ km} into metres and centimetres.

Solution:

Distance in m=4.5×1000=4500 mm = 4.5 \times 1000 = 4500 \text{ m}. Distance in cm=4500×100=450,000 cmcm = 4500 \times 100 = 450,000 \text{ cm}.

Explanation:

To convert kilometres to metres, multiply by 10310^3. To convert metres to centimetres, multiply by 10210^2.

Problem 3:

The thickness of a bundle of 5050 identical sheets of paper is 5 mm5 \text{ mm}. Calculate the thickness of one sheet of paper in cmcm.

Solution:

Thickness of 1 sheet=5 mm50=0.1 mm\text{Thickness of 1 sheet} = \frac{5 \text{ mm}}{50} = 0.1 \text{ mm} In cm: 0.110=0.01 cm\text{In cm: } \frac{0.1}{10} = 0.01 \text{ cm}

Explanation:

Divide the total thickness by the number of sheets to find the thickness of one sheet, then convert mmmm to cmcm by dividing by 1010.