POSITIONAL NUMBERS – PLACING THE NUMERALS

Introduction

Numerals denote the number in the form of symbols. When these symbols help the number to gain a position and indicate the value of the number then it is said to be positional numbers. Talking about the time when the stone age people used woods and bones to tally and count, to the time when people started using mathematics, solving practical problems of algebra, using elementary geometry for civilization out the lives of people and helped in the evolution of mathematics.

Evolution of number system

The numeration system came into existence in the 6th century BCE when different number systems of base 10, base 20, base 60, and other base systems were used in different parts of the world. Here the question arises what exactly do they mean?

  1. Base 60 number system: – this number system was derived by Babylonians in 4000 BCE. They used a complex structure to build a number system. Sexagesimal means the number system with base 60 where the reasonings to choose base as 60 is still unknown. the facts that they noticed as the possible reason was 60 is a number which can be divisible by 1,2,3,4,5,6,10,12,15,20 and 30. The symbols used to indicate the numbers were extraordinary. But this system had a lot of drawbacks. For centuries, the number system was without any place value holder and had nothing to separate whole numbers from fractional parts. However, to indicate the values as placeholder zero today, this was the earliest try to use zero in the number system.
  2. Base 20 number system: – this number system was widely used in parts of Europe, Africa, and Asia when it came into existence in the 1st millennium BCE. The vigesimal i.e., base 20 number system probably evolved from simple counting using fingers and toes. However, the numerals for this number system were symbolled as rods. E.g., if the number is 45 then 4*(10) ^1 are represented as horizontal lines, and 5*1 is represented as vertical lines.
  3. Base 10 number system: – This number system actually turned the tables in mathematics. But the question is how is it introduced?
  4. A number system is required to record quantifiable information.
  5. It is impractical to give a symbol to every number.
  6. By placing the same symbol in different positions, information is conveyed efficiently.
  7. The numerical value of the symbol helps to indicate the position of the number. 
  8. Only ten symbols are needed to represent every number.

This numeration system that is employed today is the base 10 system. In this system, 10 symbols were used i.e., 1,2,3,4,5,6,7,8,9 and 0 as place holder. As in the Babylonian system, the smallest digit value of the number is always to right. E.g., 45- 4 is tens place which means 40 and 5 are once i.e., just 5. So, the number at the right is always smaller in the number system. Placing the digits after this number will lead to hundreds, thousands, and large powers of 10. A symbol is introduced to separate the whole numbers from the fractional part, each representing tenth of the place value of the preceding figure.

  1. Other base number systems: – with increasing electronic technologies, other base systems came into use as base 2 systems. This base system has just 2 symbols 0 ad 1. Unlike the base 10 system, this is multiplied by 2 instead. So, the numbers are denoted by 2^1,2^2, etc. the number 1100 in binary is expressed as 1*2^3+1*2^2+1*2^1+1*2^0 i.e., 12 in the decimal system. The uniqueness of the modern base system is that, whatever is their base, the place values of principles are always the same.

Conclusion

“The fact that we work in 10s as opposed to any other number is purely a consequence of our anatomy. We use our ten fingers to count” by Marcus du Sautoy, a British mathematician. The positional number system is derived from various trials and errors where a lot of mathematicians from all over the world tried to define and give the numeric to the world. but the great era of 6000BCE to 500 BCE gave us this first every basic concept. Without these numerals currently, we might have been using some vertical lines or funny symbols to indicate numbers.