__maths__>__Mensuration : Length, Area, and Volume__>__Introduction 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 `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. .

*slide-show version coming soon*