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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.

## 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.