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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.continue
mathsMensuration : Length, Area, and VolumeIntroduction to Measurements

Accurate measure and Approximate measure

In this topic accuracy of measurement is explained.



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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. approximate length 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.approximate length 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.approximate 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. approximate length 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 `2`cm is possible. That object, when magnified and measured with high accuracy, will be of length `2`cm 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 `3.78023cdots`cm 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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