Numbers are invented long back but there is a difference in the placement of commas in the numerals. There are many ways of representing an integer. The best-known method is the decimal number system. The systems of numerations include mixed-radix, factorial representation. The system of numeration is also known as the Number system or numeral system.

There are different types of number systems likewise Roman, Greek, Arabic, Binary, Decimal, Hindu-Arabic, Egyptian, Babylonian, etc. This article is about expressing different types of numeral systems, solved problems on systems of numeration here. Thus check out this page and know the importance of systems of numeration.

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## Systems of Numeration – Definition

A numeral is a written symbol used to represent a number. The systems of numeration consist of a set of numerals and a rule for combining them to represent the numbers. The symbols used in the Hindu-Arabic system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the decimal point ‘.’ The systems of numeration that is used all over the world is the Hindu-Arabic system. The decimal is a place value system with base ten.

### Different Types of Numeration System

The systems of numeral systems are of many types. The well-known numeral system is Roman Numeral System or Hindu-Arabic Numeral System. Study the following systems of numerals to enhance your knowledge.

1. Hindu-Arabic Numerals System

2. Tally Numerals System

3. Egyptian Numerals System

4. Roman Numerals System

5. Babylonian Numerals System

6. Mayam Numerals System

7. Additive Numeral system

8. Place Value Systems

**1. Hindu Arabic Numerals System: **

Hindu-Arabic Number System is a set of ten symbols that represents a decimal number system. The Hindu-Arabic Number Systems are the standard systems that are used even today which include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Learn the numbers and compare them with the other systems of numeration.

**2. Tally Numerals system:**

This is the simplest of all the number systems. The tally number systems are usually seen in the concept of statistics.

**3. Egyptian Numerals system:**

The system uses symbols such as fish, lotus flower, and so on to represent the numbers.

**4. Roman Numerals System:**

Roman Numbers are the symbols that represent the Hindu-Arabic Number System. The Roman Numbers are seen to write the page numbers.

**5. Babylonian Numerals System:**

It uses only two symbols to represent the possible numbers.

**6. Mayan Numerals System:**

It uses three basic symbols which is one of the most sophisticated and complicated of all the systems of numeration.

**7. Additive Numeral system:**

In an additive system of numeration, symbols are given for groups of ten and powers of ten. The value of a combination of symbols is simply the sum of the values of each symbol used. Base-10, Base-5, Base-2, Base-12 are additive systems. These additive systems of numerations are used in computer systems.

**8. Place Value Systems:**

A place value system is one in which the position of a digit in a number determines its value. The place value system represents the value of the particular digit like ones, tens, hundreds, etc.

### Importance of Systems of Numeration

A number system is a set of values that is used to represent the quantity.

1. The system of numeration is used in our everyday life.

2. It helps to count the money.

3. Roman Numerals are used in class numbers, index pages.

4. The place value systems like binary, decimal, hexagonal values are used in the computer systems.

5. Roman symbols are used to represent numbers.

### Problems on Numeral Systems

**Example 1:**

Write the Roman number MCMCCXLVI as a Hindu-Arabic number.

**Solution:**

Divide the Roman Number into separate powers of ten, starting from the left.

Then translate each set of symbols into its corresponding Hindu-Arabic Number System.

MCMXLVI = M CM XL VI

= (1 × 1000) + (1000 – 100) + (50 – 10) + (5 + 1)

= 1000 + 900 + 40 + 6

= 1946

**Example 2.**

Write the number 103 in Egyptian Numerals.

**Solution:**

**Example 3.**

Express the number 1024 in Ruman Numerals.

**Solution:**

Roman Numerals is a number system that uses a combination of letters to express a number.

First split the numbers

1024 can be written as follow

1024 = 1000 + 20 + 4

1000 can be written as ‘M’

10 can be written as ‘X’

1 can be written as ‘I’

4 in Roman Numbers can be written as ‘IV’

Thus 1024 in Ruman Numerals can be written as MXXIV.

**Example 4.**

Write the binary number 1010 in Hindu-Arabic Numeration System.

**Solution:**

1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2^{0}

8 + 0 + 3 + 1 = 12

Thus 1010 in Hindu-Arabic Number System is 12.

**Example 5.**

Write the number 3846 in Roman Numerals.

**Solution:**

3846 = 3000 + 800 + 40 + 6

3846 = 3000 + (500 + 300) + (50 – 10) + (5 + 1)

1000 can be written as ‘M’

500 can be written as ‘D’

100 can be written as ‘C’

50 can be written as ‘L’

10 can be written as ‘X’

1 can be written as ‘I’

6 in Roman Numbers can be written as ‘VI’

Therefore 3846 = MMMMDCCCXLVI

### FAQs on Number System

**1. What are the different systems of numeration?**

- The Decimal System
- Base-Five Numeration System
- The Base-Two, or Binary, System
- The Base-Twelve, or Duodecimal, System
- Converting from One Base to Another
- Hindu-Arabic and Roman Numeral Systems
- The Real Numbers

**2. What is base 8 called?**

The octal numeral system, or oct for short, is the base-8 number system and uses the digits 0, 1, 2, 3, 4, 5, 6 and 7.

**3. Write any two types of Place Value System of numeration?**

The binary (base 2), octal (base 8), and hexadecimal (or base 16) are some types of place value numbering systems are used in computers.