In Mathematics, it is required to convert the units while solving many problems. To carry out the required calculations, mathematical conversions are needed. For example, to find the area of a triangle, if a base is given in cm, and height is given in meter, and you are asked to find the area of a triangle in cm, it is necessary to convert the height in meters into centimetres. Therefore, it is necessary to learn the conversion of units, to convert a unit into the required unit.

## What is Conversion of Units?

The use of a unit depends on the situation, such as the area of a room is expressed in meters but the length of a pencil is expressed in centimetres and its thickness in mm.

Thus, we need to convert one unit to another. Before understanding the concept of conversion of units we need to understand the relationship between units.

### Length and Mass conversion

Mensuration is an ancient concept. Every physical quantity like length, mass, time, temperature etc, have a specific unit. By definition, a unit is a magnitude of a physical quantity.

There are **two systems of units**:

- SI units (International System of Units)
- Metric system

**For example**, SI unit of length is a metre (m), while metric units are kilometre (km), meter (m), decimetre (dm), centimetre (cm) and millimetre (mm).

SI unit of mass is Kilograms (kg).

## Importance of Mathematical Conversions

In order to have accuracy and avoid confusion in measurement, we need to convert one unit to another. For instance, we do not measure the length of a pencil in kilometres, in such case one have to convert kilometre (km) to centimetre (cm). Generally, the conversion of one unit to another unit of the same quantity is performed using multiplicative conversion factors. Let’s see how to convert a different unit of length and mass.

### Table for Length Conversion

The table for conversion of length is:

The table for length conversion is given in the figure above. The relation between the adjacent unit varies by the multiple of 10 (moving left to right) and vice-versa (i.e. moving right to left).

Example: Convert 2 mm to dam.
Solution: Given 2 mm length. From the length conversion table, we see dam is 4th position left to mm. Thus, dividing the given length by 10 ⇒ 2 mm = 2/10 ⇒ 2 mm = 0.0002 dam |

### Table for Mass Conversion

Similarly, we have mass conversion table which is as follows:

## Unit Conversion Table

Let’s have a look at some basic unit conversion of mass and length.

Units of Length | Units of Mass |
---|---|

1 km = 10 hm
= 100 dam = 1000 m |
1 kg = 10 hg
= 100 dag = 1000 g |

1m = 10 dm
= 100 cm = 1000 mm |
1 g = 10 dg
= 100 cg = 1000 mg |

1 dm = 10 cm
= 100 mm |
1 dg = 10 cg
= 100 mg |

1 cm = 10 mm | 1 cg = 10 mg |

From the table above we have seen values of units of length are not the same i.e. 1 km ≠ 1m. When 1 km is equal to 1000 m that means we need 1000 meters to make up one kilometre. This makes kilometre a bigger unit than a meter. This is same for 1 kg = 1000g. Conversion of units can be done in a few steps.

**Points to remember:**

- To convert bigger units to a smaller unit multiply.
- To convert a smaller unit to a bigger unit divide.

### Conversion of Units Solved Examples

Example 1: Convert 2 cm to km.
Here we want to convert Since km is the larger unit, thus put 1 under the corresponding column (km).
Here we want to convert cm to
We see the conversion is from a smaller to a larger unit. Thus, we need to divide the given length by 100000 (i.e. 10 2cm = 2/10 ⇒2cm = 0.00002 km
We know, 1 g = 1000 mg Thus, 5 g = 5 × 1000 = 5000 mg |

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