Renard Series for Currency Denominations (Important) (Download PDF)

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Countries use the Renard series for convenient use of currency where the ratio between adjacent denominations of currencies is 1: 2 or 1: 2.5. The denomination should be twice or two-and-half times of its preceding denomination allowing exchange of value ordinarily in a maximum of three denominations.

Image of Renard Series for Currency Denominations

Image of Renard Series for Currency Denominations

Image of Renard Series for Currency Denominations

1 - 2-5 Series- RBS’S Variation on Renard Series

  • To determine Indian currency denominations, RBI follows a variation of the Renard Series, called the 1 - 2-5 series where a ‘decade’ or a 1: 10 ratio is covered in 3 steps.

  • First number in the series would be 1, the second would be 2, and the third would be 5. Thus we have currency notes of 1,2, 5,10,20,50,100,200,500,1000, …etc.

  • New bright yellow 200-rupee the missing link in the RBI’s modified Renard Series.

Maths of Renard Series

  • Renard series is a system of preferred numbers dividing an interval from 1 to 10 into 5,10,20, or 40 steps.

  • Proposed in the 1870s by French army engineer Colonel Charles Renard

  • System adopted in 1952 as an international standard ISO 3.

  • Factor between two consecutive numbers approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58,1.26,1.12, and 1.06, respectively producing geometric sequence).

  • Maximum relative error is thus minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.

  • Applications of the Renard series includes current rating of electric fuses and those of resistance used in electrical circuits.

  • Most basic R5 series consists of five rounded numbers powers of the fifth root of 10, rounded to two digits: R5: 1.00 1.60 2.50 4.00 6.30

  • For finer resolution another five numbers are added, one after each of the original R5 numbers producing R10 series rounded to a multiple of 0.05.

- Published/Last Modified on: September 6, 2017

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