March 22, 2021

Chapters

These units of measurement were used in England up to 1826 and were later replaced by imperial units. The imperial units were a mixture of the Roman system of units and Anglo-Saxon. Different standards were applied to these units at different times that were used for various applications.

The two primary sets of English units were Winchester Units and Exchequer standards. Winchester units were used from 1495 to 1587, while Exchequer standards were used from 1588 to 1825. Imperial units replaced these standards in 1824.

Although the United States accepted the metric system in 1866, however, the US has still not adopted the metric system as its official system of measurement. People in the US used the English system in their daily measurement which is the reason why the English system is still prevalent in the US. The English system helps to measure the bigger units without the need for external measuring tools. For example, the human foot can be used to measure the shorter ground distances and paces can be used to measure the long distances. Traditionally, people used to measure capacities through cups, pails, and baskets.

Now, that you are familiar with the history of the English system of measurement, let us see what are its units of length, capacity, mass, and area under the English system of measurement.

### Units of Area

**Inch** = 2.54 cm.

**Foot** = 12 inches = 30.48 cm.

**Yard** = 3 feet = 91.44 cm.

**Fathom** = 2 yards = 1.829 m.

**Statute mile** = 880 fathoms = 1.609 km.

**Nautical mile **= 1,852 m.

### Units of Capacity

**Pint ** (UK) = 0.568 litres

**Pint ** (U.S.) = 0.473 litres

**Barrel **= 159 litres

### Units of Mass

**Ounce** = 28.3 grams

**Pound ** = 454 grams

### Units of Area

**Acre** = 4,047 m²

## Metric System

The metric system of measurement was implemented after the decimalized system in the 1790s. The evolution of these systems resulted in the definition of the International System of Units (SI) which is managed by an international standard body.

The metric system has gradually evolved. This evolution culminated in the recognition of many principles. Nature has many dimensions and each of the primary dimension of nature are represented by one base unit. The base units are defined based on natural principles instead of physical artifacts. Before the metric system, every country was using a different system of measurement which made business relations between different nations extremely difficult. The Academy of Sciences in Paris proposed this system in 1792 which was adopted by all countries except, Burma, Liberia, and the United States.

Now, let us see what are units of length, mass, capacity, and area under the Metric system.

### Units of Length

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 |

### Units of Mass

Grams

### Other Units of Mass

1 tonne (T) | 1000000 grams |
---|---|

1 kilogram (kg) | 1000 grams |

1 hectogram (hg) | 100 grams |

1 decagram (dag) | 10 grams |

1 decigram (dg) | 0.1 grams |

1 centigram (cg) | 0.01 grams |

1 milligram (mg) | 0.001 grams |

### Units of Capacity

Liters and milliliters

### Other Units of Capacity

Kiloliter (kl) | 1000 liters (l) |
---|---|

Hectoliter (hl) | 100 liters (l) |

Decaliter (dal) | 10 liters (l) |

Deciliter (dl) | 0.1 liter (l) |

Centiliter (cl) | 0.01liter (l) |

Milliliter (ml) | 0.001 liter (l) |

### Units of Area

Square meter

### Other Units of Area

square kilometer | km² | 1,000,000 m² |

square hectometer | hm² | 10,000 m² |

square decameter | dam² | 100 m² |

square meter | m² | 1 m² |

square decimeter | dm² | 0.01 m² |

square centimeter | cm² | 0.0001 m² |

square millimeter | mm² | 0.000001 m² |

## Conversion of Units

Let us now solve some examples in which we will convert one unit into another.

## Example 1

How many yards are there is 56 feet?

### Solution

We know that in 1 yard there are 3 feet.

1 yard = 3 feet

56 feet = x yards

56 feet = yards

56 feet = 18.66 yards

## Example 2

It takes 2908 liters of water to fill up the well to its full capacity. How many barrels of water are needed to fill up the well?

### Solution

1 barrel = 159 liters

2908 liters = x barrels

2908 liters = barrels

2908 liters = 18.3 barrels

## Example 3

Sarah needs 12 ounces of sugar, 2 ounces of salt, 24 ounces of flour, and 3 pints (U.K) of milk. How much of these items are needed in grams and liters?

### Solution

Sugar needed for cake in ounces = 12

1 ounce = 28.3 grams

12 ounces of sugar = 12 x 28.3

= 339.6 grams

Salt needed for cake in ounces = 2

1 ounce = 28.3 grams

12 ounces of sugar = 2 x 28.3

= 56.6 grams

Flour needed for cake in ounces = 24

1 ounce = 28.3 grams

12 ounces of sugar = 24 x 28.3

= 679.2 grams

Number of pints (U.K) of milk needed to bake a cake = 3

1 Pint (UK) = 0.568 liters

3 pints (UK) = 3 x 0.568

= 1.704 liters

## Example 4

Before the party, Sarah bought 20 bottles of water. Each bottle can hold 2.5 liters. How many pints (US) of water are present in all the 20 bottles?

### Solution

Total number of bottles = 20

The capacity of water in a single bottle = 2.5 liters

The capacity of water in 20 bottles = 20 x 2.5 liters

= 50 liters

1 Pint (U.S.) = 0.473 liters

50 liters = pints

= 105.67 pints

The next three problems will be about the metric system of measurement.

## Example 5

Convert 12,000 into mm^2m^2mm^2m^2m^2\frac {1}{1000000} mm^2mm^2\frac {12000}{1000000} m^2m^2\frac {1}{3} \times 51 = 17$ dal

The capacity of both the water tanks to hold water to their full capacity = 51 + 17 = 69 dal

1 dal = 10 liters

Amount of water in both the tanks if they are filled to their full capacity = 69 x 10 = 690 liters.

Hence, 690 liters of water are present in both tanks.

## Example 7

An athlete covered a distance of 8 km, 0.75 hm 12 dam on his bicycle. His fellow covered a distance of 8000 m 2 hm and 8 dam on his bicycle. Who traveled the longest distance?

### Solution

To tell the longest distance traveled, we should convert the distances covered by both the athletes into one unit. Let us convert the distances covered by both the athletes in meters.

Distance covered by the first athlete = 8 km 0.75 hm 12 dam

1 kilometer = 1000 meters

8 kilometers = 8 x 1000 meters

= 8000 meters

1 hm = 100 meters

0.75 hm = 0.75 x 100

= 75 meters

1 dam = 10 meters

12 dam = 12 x 10 meters

= 120 meters

Total distance covered by first athlete in meters = 8000 + 75 + 120 = 8195 meters

Distance covered by second athlete = 8000 m 2 hm 8 dam

1 hm = 100 m

2 hm = 2 x 100 = 200 m

1 dam = 10 m

8 dam = 8 x 10 = 80 m

Total distance covered by second athlete in meters = 8000 + 200 + 80

= 8280 meters

Now, let us compare the distance covered by both the athletes. The first athlete covered a distance of 8195 meters and the second athlete covered the distance of 8280 meters. Hence, we can say that the second athlete covered more distance than the first athlete.