Length: Definition and Meaning of a Length, Tools for Measuring Length, Metric System and Customary System (For CBSE, ICSE, IAS, NET, NRA 2022)

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Definition and Meaning

  • Length is simple words is the measure of distance.
  • It is also defined as a quantity with dimension distance in the International System of Quantities.
  • The base unit for length is the metre in the International System (SI) of Units.
  • The commonly used units of length are the inch (in) , the foot (ft) , the yard (yd) , and the mile (mi) in U. S. customary units, English, or Imperial system of units.
  • It is the measure of one spatial dimension. Area is a measure of two dimensions and Volume is a measure of three dimensions.
  • Various terms for the length of a fixed object are used:
    • Height, which is vertical length or vertical extent.
    • Width, breadth, or depth.

Metric Length and Imperial Measurement

Metric Length and Imperial Measurement

The metric length of one kilometer is equivalent to the imperial measurement of 0.62137 miles.

History

  • Measurement has always been an important aspect of life ever since humans settled from nomadic lifestyles.
  • This further includes using building materials, occupying land and trading with neighbors.
  • The need for standard units of length increased with increase in trade between different places.
  • Length of a foot, width of a palm, etc. were used as units for the measurement of length in ancient times.
  • β€˜Cubit’ one of the oldest methods of measurement of length is the length of the arm from elbow to the finger tips. However, these units differ from person to person.

The International System of Units (SI)

  • To maintain uniformity in measurements a set of standard units of measurements have been accepted all over the world.
  • Centimeter – gram – second system of units wherein the fundamental unit of length is centimeter.
  • Kilometer is used as the unit of length for measuring large lengths.

Tools for Measuring the Length

  • Vernier caliper
  • Tapes

Relationship between Different Units of Length

Relationship between Different Units of Length
1 kilometre (km)10 Hectometres (hm) = 1000 m
1 Hectometre (hm)10 Decametres (dcm) = 100 m
1 Decametre (dcm)10 Metres (m)
1 Metre (m)10 Decimetres (dm) = 100 cm = 1000 mm
1 Decimetre (dm)10 Centimetres (cm)
1 decimeter0.1 meter
1 Centimetre (cm)10 Millimetres (mm)
1 centimeter0.01 meter
1 millimeter0.001 meter

Customary Units of Length

Customary Units of Length
1 mile1760 yards
1 mile5280 feet
1 yard3 feet
1 foot12 inches

Use in Mathematics

Euclidean Geometry

  • One of many applications in Euclidean geometry is that of Pythagoras Theorem relating the length of the sides of a right triangle.
  • In Euclidean geometry, length is measured along straight lines.
    • Unless otherwise specified and refers to segments on them.

Other Geometries

  • Length may be measured along possibly curved paths, called geodesics.
  • Length is measured along the great circles on the sphere in spherical geometry.

Graph Theory

  • In an unweighted graph, the length of a cycle, path, or walk is the number of edges it uses.
  • In a weighted graph, the length may be the sum of the weights of the edges that it uses.
  • Between two vertices in a graph, length is used to define the shortest path, girth (shortest cycle length) , and longest path.

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