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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsMensuration : Length, Area, and VolumeIntroduction to Measurements

### Accurate measure and Approximate measure

In this topic accuracy of measurement is explained.

click on the content to continue..

Consider a pencil. How to measure the length of a pencil?

• mark the ends of the pencil into a line-segment and measure the length of the line-segment
• measure the distance-span between the two ends of the pencil
• either one of the above
• either one of the above

The answer is "either one of the above".

To measure the length of a pencil, an equivalent line segment is taken. The line segment and the graduated scale are shown in the figure. Note the legend on the right-top of the figure showing 1 centimeter. What is the length of the line segment bar(AB)?

• length cannot be found
• 2.7cm
• 2.7cm

The answer is "2.7cm".

The figure is magnified. Note the legend showing the modified 1cm length. The point A is not shown. As per the figure, Which of the following is correct?

• the length of bar(AB) is accurately 2.7cm
• the length of bar(AB) is approximately 2.7cm
• the length of bar(AB) is approximately 2.7cm

The answer is "the length of bar(AB) is approximately 2.7cm"

The figure is magnified even larger. Note the legend showing the modified 1mm length. As per the figure, which of the following is more accurate?

• the length of bar(AB) is still 2.7cm
• the length of bar(AB) is better approximated to 2.78cm
• the length of bar(AB) is better approximated to 2.78cm

The answer is "the length of bar(AB) is better approximated to 2.78cm"

The line-segment bar(AB) can be measured at different accuracies.

•  The length is 2.7cm when measured with a scale.

•  The length is 2.78cm when magnified and measured with a better instrument than a scale.

•  The length is 2.78892cdots when measured at much higher accuracy. For most practical applications, the length of 2.7cm is good enough. Note 1: The line represents a real object. It can be a leaf, or a rod. The important point being, the measurements in real-life are approximated.

Note 2: The length of a real object can be exactly measured too. For example, a pencil of length exactly 2cm is possible. That object, when magnified and measured with high accuracy, will be of length 2cm only.

Note 3: The length of a real object can be a decimal number, that does not end or does not repeat. For example, a pencil is of length 3.78023cdotscm length. The decimals in the number does not end or repeat. It is an interesting observation, that will help to understand some concepts later.

Which of the following is a meaning for the word "accuracy"?

• state of being exactly correct
• state of being exactly correct
• gather together in large numbers

The answer is "state of being exactly correct".

What is the term used to refer "state of being exactly correct"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "accuracy".

Accuracy of Measurements : Measurement can be performed to a desired accuracy level.

When the accuracy is specified to a lower level, the measurement is approximate measurement. .

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