# Number System in Mathematics and Its Usage in Modern Life

The number system is a fundamental concept in mathematics. Mathematics is required to prove scientific things, and numbers are required for mathematical calculations. In mathematics, numbers usually refer to integers. There are two types of numbers: divisible and indivisible. If you can divide a number into equal parts by integers, these are called divisible numbers. On the other hand, if you can not divide a number by an integer, it is called an indivisible number.

## What is a number system?

Numbers can have different bases in the number system. The most prevalent system is the decimal or 10-base system. Binary or 2-based number systems and hexadecimal or 16-based number systems are available.

In ancient times, when communication was limited, different number systems were popular from country to country. The method of counting or measuring in one country did not match another. Expressing numbers and calculations was as diverse and unique as languages.

The decimal number system gained popularity with the advancement of international communication and commerce. At that time, what was commonly used in arithmetic calculations, known as arithmetic progression, was prevalent in the decimal system. Later, with the advent of computers, binary and hexadecimal systems were discovered. Additionally, in ancient Babylonian civilization, the octal number system, 40-based number systems, and 16-based number systems were popular in agricultural societies.

## Decimal Numbers:

The decimal number system is the basis of ordinary arithmetic calculation. The numbers of 0 to 9 are the basis of the decimal system. In general mathematics, such as arithmetic, algebra, and geometry, the decimal system is used to do addition (+), subtraction (-), multiplication (*), and division (/).

## Binary Numbers:

The fundamental principle of computer systems is based on the binary number system. This system uses only 0 and 1 to represent numeric values. We know that a computer is an electronic device. And this device can only understand whether there is electricity or no electricity. And it is expressed through the two numbers 1 and 0. So, in the binary system, although the value of 1 is 1, for 2, it will be 10 in binary, and for 3, it will be 11. The binary arithmetic operations use only 1 and 0 for addition, subtraction, multiplication, and division, similar to decimal operations.

## Hexadecimal Numbers:

The hexadecimal number system is a 16-based number system. In this system, in addition to 0 to 9, the first six English letters are used. So, in the decimal system, the value of 15 is represented in the hexadecimal system by the English letter F. Arithmetic operations are similar to those in the decimal system. Still, after addition, the result is written by subtracting 16 from the decimal value.

## Octal Numbers:

In ancient civilizations, the octal number system was prevalent. And even now, its usage is seen in some fields of mathematics. In the octal system, eight numbers from 0 to 7 are the basis, and the number after 7 is 10, whose value in decimal is 8. The octal system has no number character as 8, so the number after 7 depends on two numbers. In the octal system, the value of 20 is 16 in decimal. Due to its proximity to decimal numbers, the octal system is often used in computer systems (such as Linux) for easy representation.

## Roman Numbers:

The Roman numeral system is the most extensive numerical system in the world. This system represents numbers through separate English letters, with five as the basis. Roman numbers have individual units up to 1000. Although the Roman numeral system is not commonly used now, it is sometimes based on decimals.

## Scientific Notation:

Scientific notation is commonly used in scientific calculations to represent large numbers. In this notation, non-numeric characters and indices are used. For instance, when the index of k is used, it means that the number k will be multiplied k times. Now, if k is 10 and m is 3, then the index k m represents the value of k multiplied by itself three times, which gives us a result of 1000. This way, large numbers that would otherwise be difficult and prone to error to write in standard form, can be written in index form.

## Arabic and Indian Number System:

Primarily based on the decimal system, number systems were prevalent in the Arabian and Indian subcontinent. With the expansion of trade and commerce over time, this system was adopted successively by civilizations. Based on the decimal number system, various mathematical calculations developed and based on it, various research and books on mathematics were written.

### Application of Various Number Systems in Modern Life:

In our real life, we see various uses of number systems. In the Indian subcontinent, this number system is still noticeable in various calculations, such as measuring 16 annas to make one ‘Vori’, where the unit of gold measurement is ‘Vori’, with a base of 16, and each base is considered as one anna. It is used in agricultural products measurement, such as measuring 40 kg as 1 ‘mon’. Roman numbers are used in clock hands or in schools to teach classes. Besides, decimal numbers are used in mathematical calculation, in computer science, binary, octal, hexadecimal, and decimal systems are used. Mathematics is essential for accurate measurement. And the basis of mathematics is number system. So, in every aspect of modern life, number system are widely used for various measurement.