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Motion and Measurement of Distances - How do we Measure?

Grade 6CBSE

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

🔑Concepts

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Measurement means the comparison of an unknown quantity with some known fixed quantity of the same kind. This known fixed quantity is called a unit.

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In ancient times, people used non-standard units like handspan, cubit (length from elbow to fingertips), and foot. These were unreliable because they varied from person to person.

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The International System of Units (SI Units) was adopted for uniformity. The SI unit of length is the metre (mm).

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Multiples and sub-multiples of length are used for convenience: 1 km=1000 m1 \text{ km} = 1000 \text{ m}, 1 m=100 cm1 \text{ m} = 100 \text{ cm}, and 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}.

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To measure length correctly using a ruler: (1) Place the ruler in contact with the object along its length. (2) Start measuring from the 00 mark. (3) Keep the eye vertically above the point of measurement to avoid parallax error.

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If the zero mark of a ruler is broken or obscured, start from any other full mark (e.g., 1.0 cm1.0 \text{ cm}) and subtract that value from the final reading at the other end.

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To measure the length of a curved line, a thread or string is used. The thread is placed along the curve, and then the length of the thread is measured using a standard scale.

📐Formulae

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

1 m=100 cm1 \text{ m} = 100 \text{ cm}

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

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

💡Examples

Problem 1:

The distance between two cities is 3540 m3540 \text{ m}. Express this distance in kilometers (kmkm).

Solution:

We know that 1000 m=1 km1000 \text{ m} = 1 \text{ km}. Therefore, 1 m=11000 km1 \text{ m} = \frac{1}{1000} \text{ km}. To convert 3540 m3540 \text{ m} to kmkm: 3540 m=35401000 km=3.54 km3540 \text{ m} = \frac{3540}{1000} \text{ km} = 3.54 \text{ km}

Explanation:

To convert a smaller unit (meter) to a larger unit (kilometer), we divide by the conversion factor 10001000.

Problem 2:

While measuring the length of a knitting needle, the reading of the scale at one end is 3.0 cm3.0 \text{ cm} and at the other end is 33.1 cm33.1 \text{ cm}. What is the length of the needle?

Solution:

Given: Initial reading = 3.0 cm3.0 \text{ cm} Final reading = 33.1 cm33.1 \text{ cm} Length of the needle is calculated as: 33.1−3.030.1\begin{array}{r} 33.1 \\ -3.0 \\ \hline 30.1 \end{array} Length =30.1 cm= 30.1 \text{ cm}.

Explanation:

Since the measurement did not start from zero, we subtract the starting mark value from the final reading value to get the true length.

Problem 3:

A student measures a line to be 15.5 cm15.5 \text{ cm}. Convert this length into millimeters (mmmm).

Solution:

We know that 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}. To convert 15.5 cm15.5 \text{ cm} to mmmm: 15.5×10=155 mm15.5 \times 10 = 155 \text{ mm}

Explanation:

To convert a larger unit (centimeter) to a smaller unit (millimeter), we multiply by the conversion factor 1010.