## 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 kilometer (km), meter (m), decimeter (dm), centimeter (cm) and millimeter (mm).

SI unit of mass is Kilograms (kg).

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 kilometers, in such case one have to convert kilometer (km) to centimeter (cm). Generally, 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.

**UNIT CONVERSION:**

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 centimeters and its thickness in mm.

Thus we need to convert one unit to another. Before conversion of units we need to understand the relation between units:

**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).

In a similar manner we have mass conversion table which is as follows:

Example: Convert 2 mm to dam.
Solution: Given 2mm length. From the length conversion table, we see dam is 4th position left to mm. Thus dividing the given length by \(10^{4}\). \(\Rightarrow 2mm = \frac{2}{10^{4}} dam\) \(\Rightarrow 2mm = 0.0002 dam\) |

Let’s have a look at some of the 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 gd
= 100 cm = 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 same i.e. 1 km â‰ 1m. When 1 km is equal to 1000 m we mean we need 1000 meters to make up one kilometer. This makes kilometer a bigger unit than a meter. This is same for 1 Kg = 1000g. Conversion of units can be done in few steps.

Points to remember:

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

Example: Convert 2 cm to km.
Here we want to convert As km is the larger unit, thus put 1 under the corresponding column (km).
1
Here we want to convert cm to
We see the conversion is from smaller to larger unit, thus we need to divide the given length by 100000 (ie\(10^{5}\)). \(2 cm = \frac{2}{10^{5}} km\) \(\Rightarrow 2 cm = 0.00002 km\)
We know 1 g = 1000 g Thus 5 g = 5 \(\times\) 1000 = 5000 mg |

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