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In this article, we will learn what are the units of length in the metric system and how to convert one unit to another. But before proceeding to discuss the units of lengths and their conversion, let us first see what is a metric system and how it differs from the customary system.

## What is the Metric System?

This system is an international system of measurements that was adopted in France in 1795 because before this year every country has its separate units of measurements that were causing difficulties in commercial trade between the nations. After the development of this system, it was adopted by all the countries in the world except for three. These three countries were Burma, Liberia, and the United States. In many regions of the U.S, the customary system is used. In countries like the U.K, this system exists along with some other measurement systems.

In the metric system, the smaller and bigger quantities are expressed as submultiples and multiples of the standard unit. In other words, the metric system is based on powers of 10. Though the customary system is different from the metric system, smaller units are also present in it. To measure the length, the volume of a liquid, and mass, the customary system uses feet, quarts, and ounces.

## What is Length?

Length is defined as:

"Distance between two points"OR

"The maximum extended dimension of an object"

In the next section, we will see what is the SI and other units of length under the metric system.

## SI Unit of Length in the Metric System

The fundamental unit for measuring length is the **meter**.

### Other Units of Length

There are also other units for measuring large and small quantities, the most common are:

kilometer | km | 1,000 m |

hectometer | hm | 100 m |

decameter | dam | 10 m |

meter | m | 1 m |

decimeter | dm | 0.1 m |

centimeter | cm | 0.01 m |

millimeter | mm | 0.001 m |

Note that each unit is 10 times larger than the previous.

Therefore, the problem of converting units to other units becomes an issue of multiplying or dividing the unit by one followed by as many zeros as there are places between them on the table above.

### Other Measurements of Length

Other measurements of length are especially in astronomy to measure extremely long distances.

## Astronomical Unit

An astronomical unit is the mean distance from the Earth to the Sun. It is used in the measurement of orbits and trajectories inside the Solar system.

**1 UA = 149,597,871 km**

## Light-year

The light-year is equal to the distance traveled by light in one average solar year. It is used in astronomy to measure extremely large distances.

The light-year is approximately equal to:

**1 light-year ≈ 9,461,000,000,000 km**

## Parsec

A parsec is an astronomical unit of measurement corresponding to the distance between the earth and an astronomical object with a parallax angle of one second.

The parsec is approximately equal to:

**1 parsec ≈ 30,857,000,000,000 km**

## Microscopic Measurements:

## Micrometer or Micron

It is equivalent to one-millionth of one part meter.

**1 μm = 0.000001 m**

## Nanometer

Equivalent to a billionth of a meter. Used to measure ultraviolet radiation, infrared radiation, and light.

1**nm = 0.000000001m**

## Angstrom

Equal to one ten-billionth of a meter (long-short). It is the unit used primarily to express wavelengths, molecular and atomic distances.

**1Å = 0.0000000001 m**

In the next section, we will solve some examples in which we will convert one unit to another.

## Example 1

Convert 58 meters (m) to centimeters (cm).

### Solution

In this case, multiply (because m is greater than the cm) the unit by one followed by two zeros, since there are two places between both units.

1 meter = 100 centimeters

58 meters = 58 x 100

=5800 cm

## Example 2

Convert 5896 mm to meters

### Solution

In this case, divide (because the mm is smaller than the m) by one followed by three zeros, since there are three places between both units.

1 m = 1000 mm

5896 mm = m

Since a four-digit number is divided by 1 followed by three zeros, therefore, we will move the decimal point three units to the left.

= 5.896 m

## Example 3

Convert 205 cm into hectometers

### Solution

Since cm is a smaller unit and hectometer is a bigger unit, hence, we will use the arithmetic operation of division here for conversion. For our ease, we will first convert cm into meters, and then meters into hectometers (hm).

1 m = 100 cm

205 cm = m

A three-digit number is divided by 1 followed by two zeroes, so we will move the decimal point two units to the left:

= 2.05 m

Now, we have the length in meters, we can easily convert it into hectometers.

1 hm = 100 m

2.05 m = hm

The decimal point will be moved two units from the left because in the denominator we have 100:

= 0.0205 hm

## Example 4

Convert 6 km 6 hm 8 dam into meters

### Solution

In this example, we are given a complex measurement. We have to convert this complex measurement which contains multiple units into a simple measurement having a single unit. We will convert each unit separately like this:

1 km = 1000 m

6 km = 6 x 1000 m

= 6000 m

1 hm = 100 m

6 hm = 6 x 100 m

= 600 m

1 dam = 10 m

8 dam = 8 x 10

= 80 m

Now, we have three values that we have obtained after converting each unit into meters. We will take an aggregate of these three values to write the final answer in meters:

= 6000 + 600 + 80

= 6680 m

## Example 5

Mariah rode 5 km 0.5 hm 10 dam on her bicycle. Her friend Sarah rode 4000 m 1 hm 20 dam on her bicycle. Who covered the longest distance?

### Solution

To tell the longest distance covered, we need to convert the distances covered by both friends into a single unit. Let say, we choose to convert both the distances in meters.

Distance covered by Mariah = 5 km 0.5 hm 10 dam

1 km = 1000 m

5 km = 5 x 1000 m

= 5000 m

1 hm = 100 m

0.5 hm = 0.5 x 100

= 50 m

1 dam = 10 m

10 dam = 10 x 10 m

= 100 m

Total distance covered by Mariah in meters = 5000 + 50 + 100 = 5150 meters

Distance covered by Sarah = 4000 m 1 hm 20 dam

1 hm = 100 m

1 dam = 10 m

20 dam = 20 x 10 m

= 200 m

Total distance covered by Sarah in meters = 4000 + 100 + 200

= 4300 m

Now, we will compare the distance covered by both the friends. Of course, 5150 meters is greater than 4300 meters. Hence, we can say that Mariah covered more distance than Sarah.

## Example 6

John estimated the lengths of two walking tracks. The length of the first track was 5648 meters and the length of the second track was 3500 m 20 hm and 20 dam. What is the total length of two walking tracks in kilometers?

### Solution

Length of the first walking track = 5648 m

1 km = 1000 m

5648 m = m

= 5.648 km

Hence, the length of the first walking track in kilometers = 5.648 km

Length of the second walking track = 3500 m 20 hm 20 dam

Since the length of the second walking track is given as a complex measurement, therefore, we will convert it into a simple measurement to determine the total length of the two walking tracks.

1 km = 1000 m

3500 m = m

= 3.5 km

1 hm = 100 m

200 hm = 20 x 100

= 2000 m

= km

= 2 km

1 dam = 10 m

20 dam = 20 x 10 = 200 m

= km

= 0.2 km

Length of the second walking track = 3.5 + 2 + 0.2 = 5.7 km

Total lengths of the two walking tracks = 5.648 + 5.7 = 11.348 km

Hence, the combined lengths of the two walking tracks is 11.348 km.

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