Mensuration : Length, Area, and Volume : Accurate measure and Approximate measure

maths > mensuration-basics

Accurate measure and Approximate measure

what you'll learn...

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 $1$ $1$ centimeter. The length of the line segment $\bar{A B}$ $bar(AB)$ is " $2.7$ $2.7$ cm".

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

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

The line-segment $\bar{A B}$ $bar(AB)$ can be measured at different accuracies.

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

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

• The length is $2.78892 \dots$ $2.78892cdots$ when measured at much higher accuracy. For most practical applications, the length of $2.7$ $2.7$ 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 $2$ $2$ cm is possible. That object, when magnified and measured with high accuracy, will be of length $2$ $2$ 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 $3.78023 \dots$ $3.78023cdots$ 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.

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