Conversions and Transformations

In mathematics, we often need to convert one quantity into another and transform a given structure into another. These are called conversions and transformations. Conversions in any type of calculation are required to convert physical quantities from one unit system to another, like conversion in mass, length, time, etc. Transformation in a geometric shape is done by translation, reflection, dilation, and rotation.

In this article, we shall discuss these two concepts in brief.

Types of Conversions

Conversion means converting a physical quantity from a unit measurement system into another. For example, if we need to add two quantities, 2kg and 250g, we cannot perform the addition until the amounts are in the same measurement system; then, either we have to convert kilograms into grams or convert grams into kilograms. Let us see conversions among different types of physical quantities.

Length conversion

To convert a unit of length into another unit, we may use the following conversions.

Unit Conversions for Length
10 millimetres (mm) 1 centimetre (cm)
10 centimetres (cm) 1 decimetre (dm)
100 centimetres (cm) 1 metre (m)
10 decimetres (dm) 1 metre (m)
10 metres (m) 1 decametre (dam)
100 metres (m) 1 hectometre (hm)
1000 metres (m) 1 kilometre (km)
1 inch 2.54 centimetres or 2.54 × 10–2 metres
1 foot 30.48 centimetres or 0.3048 metres
1 yard 91.44 centimetres or 0.9144 metres
1 mile 1.609344 kilometres (km)

Learn more about length conversion with suitable examples.

Mass conversions

To convert a unit of mass into another unit, we may use the following conversions.

Unit Conversions for Mass
10 milligrams (mg) 1 centigram (cg)
10 centigrams (cg) 1 decigram (dg)
100 centigrams (cg) 1 gram (g)
10 decigrams (dg) 1 gram (g)
10 grams 1 decagram (dag)
100 grams 1 hectogram (hg)
1000 grams 1 kilogram (kg)
1 pound (lb) 0.453592 kilograms
1 tonne 1000 kilograms
Time conversions

This is a list of unit conversions for time, which are often needed in any calculation, like converting hours into minutes, days into years etc.

Unit Conversions for Time
1 minute 60 seconds
1 hour 60 minutes or 3600 seconds
1 day 24 hours
1 week 7 days
1 year 365 days
Area conversion

Let’s check out some conversion units for the area.

Unit Conversions for Area
1 acre 0.00404686 sq. kilometre
1 sq. inch 6.4516 x 10-4 sq. metre
1 sq. foot 9.2903 x 10-2 sq. metre
1 acre 4.0468 x 103 square metre
1 hectare 1 x 104 sq. metre
1 sq. mile 2.5888 x 106 sq. metre

Transformations are the changes introduced to the geometrical shapes by resizing (dilation), reflection, translation and rotation. Mathematical transformations are functions f: X → X, which map into the same set, such that the f-image of X differs from its preimage in terms of position, shape and size.

Transformation by dilation

This type of transformation is produced by resizing the shape by reducing or magnifying it and keeping its orientation unchanged. An example of dilation is similar figures, in which the shape remains intact, but the size may vary.

Transformation by reflection

The mirror image of any shape is the reflection transformation. These transformations produce a shape’s lateral inversion or a flipping effect, but the size remains unchanged.

Transformation by rotation

When any geometrical shape is transformed by rotating it from a fixed point along an axis, it is said to be a rotation transformation. Rotation transformations do not change the shape and size of the geometrical figure. For example, rotating a given object by 90o or 180o clockwise or anticlockwise.

Learn more about rotation here.

Transformation by translation

Translation could simply mean moving an object. If a geometrical figure is displaced in space, the transformation is said to be a translation. Translation does not change the shape, size, and orientation of the geometrical figure.

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