Accurate measure and Approximate measure

Overview

**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.

exact

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

We can directly measure the distance-span between the two ends of the pencil. OR,
we can mark the ends of the pencil onto a line-segment and measure the length of the line-segment.

To measure the length of a pencil, an equivalent line segment is formed. 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. The length of the line segment $\overline{AB}$ is "$2.7$ cm".

The figure is magnified. Note the legend showing the modified $1$ cm length. The point $A$ is not shown. It is noted that, the length of $\overline{AB}$ is approximately $2.7$ cm.

The figure is magnified even larger. Note the legend showing the modified $1mm$ length. As per the figure, the length of $\overline{AB}$ is better approximated to $2.78$ cm

The line-segment $\overline{AB}$ can be measured at different accuracies.

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

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

• The length is $2.78892\cdots$ when measured at much higher accuracy.
For most practical applications, the length of $2.7$ cm 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 $3.78023\cdots$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.

The word "accuracy" means: state of being exactly correct.

summary

**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.

Outline

The outline of material to learn "Mensuration basics : Length, Area, & Volume" is as follows.

Note: * click here for detailed outline of Mensuration (Basics). *

• ** Measuring Basics**

→ __Introduction to Standards__

→ __Measuring Length__

→ __Accurate & Approximate Meaures__

→ __Measuring Area__

→ __Measuring Volume__

→ __Conversion between Units of Measure__

• ** 2D shapes**

→ __Perimeter of Polygons__

→ __Area of Square & rectangle__

→ __Area of Triangle__

→ __Area of Polygons__

→ __Perimeter and area of a Circle__

→ __Perimeter & Area of Quadrilaterals__

• ** 3D shapes**

→ __Surface Area of Cube, Cuboid, Cylinder__

→ __Volume of Cube, Cuboid, Cylinder__