Unit, Number and Numeral. The Number Systems and Their Rules

What is Unit?

Everywhere in our daily life we come across the count of things or number of items, for example 6 pens, 12 bananas, 2 bikes etc. Let’s take “6 pens” to understand what a unit is. “6” refers to count of pens which is a number and the pens can be thought of a thing which is a type of “pen”, which is called as unit.
In one more real life scenario of 5 pears in a basket, there is a thing pear and the number of items of type pear are 5. One pear or a pear is a single thing, which is also called a unit.

By definition, a unit is something that denotes a single thing.

What is Number?

Again consider the example of 5 pears in the basket. So a pear is taken five times. Or in other words, a unit (which is pear here) has been taken 5 times, so 5 is called a number.

By definition, a number denotes how many times a unit is taken.

A visit to the shop is worth to see the real life examples of unit and number.
The customers buy items in numbers and pay the price for the items to the shopkeeper again in numbers.
If a customer bought 6 pens, 12 chocolates and 2 sandwiches then 6, 12, 2 are the numbers.
If the customer paid the price $4 for pens, $10 for chocolates and $5 for sandwiches, then 4, 10 and 5 are the examples of numbers.

What is Numeral?

In the above example 1, the number “nine” was used in “Joseph is nine years old”. The number “nine” can be represented using some symbols. Such symbols which can be used to represent the “nine” are called as numerals. In this case “nine” is represented with symbol 9, which is a numeral.

By definition, a numeral is a symbol which is used to represent a number.

What are the Numeral Systems?

It is a system used to write numbers using a set of symbols. From the history of mathematics, there were many mathematicians who developed many such systems. The two such famous systems are Roman Numerals and Hindu Arabic System. The Hindu Arabic Number system is the most widely accepted system in the world to write numbers.

1. Hindu Arabic Numeral System

It is the most adapted system in the world. This system was invented by Indian mathematicians between the Ist and 4th centuries. Arabs also started using this system in their Arabic mathematics but after 500 years.
Europeans started calling by another name of “Arabic numerals” also when Arabs introduced them the Hindu numerals.

In this system, numerals are represented by the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Hindu Arabic Numerals

2. Roman Numeral System

This system was invented by Romans. They used 7 letters of Latin alphabets to represent numbers. Each of the letters has a number value. Different combinations of Roman letters can be used to represent any mathematical number.

Roman numerals with their number value

Roman numeral system has no symbol for zero.

Convert Romans into Hindu Arabic

There are two following rules to convert a Roman numeral to Hindu Arabic numeral:

1. Additive notation
2. Subtractive notation

1. Additive Notation

In this notation, the Roman numerals next to each other are added up. There are two cases when these are added up.

First case is when the numerals are repeated next to each other.
For example, II, here I is repeated two times next to each other. So, they will be added up which makes 1 + 1 = 2.

Second case is when a greater numeral is followed by another smaller numeral.
For example, in VI, V has value of 5 and I has a value of 1. So, V is greater than I and V is followed I. Therefore, V and I are added up as 5 + 1 = 6. So, VI is number 6.

In additive notation, the numerals next to each other are added up when:
1. they are repetitive
2. the first numeral is greater than the second on its right

2. Subtractive Notation

In this notation, the numerals are subtracted. When a smaller numeral is followed by another greater numeral, the smaller is subtracted from the greater. For example, in IV, V has value of 5 and I has a value of 1. So, the smaller I is followed by the greater V. Therefore, I is subtracted from V as 5 – 1 = 4. So, IV is a number 4.

10 is written as X not VV because V can not be repeated.
Also, 100 is written as C not LL because L can not be repeated.

In subtractive notation, the numerals next to each other are subtracted, when: the first is smaller than the next numeral on its right.

Important rules for roman numbers

There are some following rules those must be followed while forming any roman number.

1. Only I, X, C and M can be repeated in a number.
   XX = 10 + 10 = 20 ✅
   II = 1 + 1 = 2 ✅
   VIIII = 5 + 1 + 1 + 1 + 1 = 9 ❌
2. I and X can be repeated maximum three times only.
   XXI = 10 + 10 + 1 = 21 ✅
   VII = 5 + 1 + 1 = 7 ✅
   XIIII = 10 + 1 + 1 + 1 + 1 = 14 ❌
3. Symbols V, L and D are never repeated.
   VV = 5 + 5 = 10 ❌
   CC = 100 + 100 = 200 ✅
4. V, L and D are never subtracted.
   XC = 100 – 10 = 90 ✅
   VX = 10 – 5 = 5 ❌
5. The symbol X can be subtracted from L, M and C only.
   XL = 50 – 10 = 40 ✅
   XD = 500 – 10 = 490 ❌
6. The symbol I can be subtracted from V and X only.
   IX = 10 – 1 = 9 ✅
   IL = 50 – 1 = 49 ❌
7. The symbol C can be subtracted from D and M only once.
   CD = 500 – 100 = 400 ✅
   CM = 1000 – 100 = 900 ✅
   CCD = 500 – 100 – 100 = 300 ❌
8. If a bar is placed over a numeral, that shows that it will be multiplied by 1000.
   V = 5 × 1000 = 5000 ✅
   X = 10 × 1000 = 10000 ✅

List of Hindu arabic numerals

List of Roman numerals