Everywhere in our daily life we come across hearing or visualising the count of things or number of items, for example 6 pens, 12 bananas, 2 bikes etc.
If it is a shop it is the number of things a customer buys or a price the shopkeeper is selling the grocery items. What is common that we see in counting things? It is the number always e.g. 6 or 12 or 2 etc. and what is the type of things that we are counting here is like pens, bananas and bikes.
Let’s take another example to know it better, there are 5 pears in a basket. So, here we have a thing to be counted as pear. One pear or a pear is a single thing we can think of, which is also called a unit. In this example, there are 5 pears which tell that a pear is taken five times, or in other words, a unit is taken 5 times, so 5 is called a number. So, a number is “how many times a unit is taken”. By definition, a unit is something that denotes a single thing.
A pen, a girl, a day etc.
So, here a pen is a single thing, which is a unit.
As explained above, 5 pears denote a unit which is taken 5 times. Here, the unit is a pear and it is taken as 5 in numbers. By definition, a number denotes how many times a unit is taken.
Joseph is sixteen years old.
There are seven days in a week.
In the above two examples, what are the numbers? Let’s understand them one by one.
Joseph is sixteen years old. First we find out which is a unit here? Here, the unit is a year which is a single thing.
How many times the years are taken i.e. 16 times. So, 16 is a number.
There are seven days in a week. Similarly, here, a unit is a day which is a single thing.
How many times the days are taken i.e. 7 times. So, 7 is a number.
This is how units and numbers are useful to represent any quantity of anything.
We learnt about the number which is five in “five pears” or six in “six pens”. So, in mathematics which symbols we can use to represent the five and six, these are called as numerals and in this case five is represented with numeral 5 and six with symbol 6.
By definition, a Numeral is a symbol which is used to represent the number.
Four is represented by the symbol 4 which is a numeral.
A numeral system is a system used to write numbers using a set of symbols. If we explore the history of mathematics, we could find mathematicians have developed many systems to write numbers. Majorly, the two systems are in use in world to represent numerals, one is using Roman Numerals and another is using Hindu Arabic System. The most widely accepted system to write numbers is using Hindu Arabic Number system.
The above example to write number four as 4 is a Hindu Arabic numeral. Let’s learn both numeral systems one by one.
Hindu Arabic Numeral System is the most adapted system in the world to represent a number. This system was invented by Indian mathematicians between the Ist and 4th centuries. After 500 years Arabs started using the system in their Arabic mathematics. Europeans started calling it as Arabic numerals also when Arabs introduced them to Hindu numerals.
In Hindu Arabic numerals are represented by symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as shown below in figure. We are already familiar with these numbers too from our daily life. This system to write numbers is based on place value system.





Roman numerals are invented by Romans. Romans used 7 letters of Latin alphabets to represent numbers. Each letter in the Roman numeral system has a number value also. So, we can convert Roman numeral into numbers, even different combinations of Roman letters can be used to represent any mathematical number. Following is the list of Roman symbols, each of which has a value in numbers also. We can see Roman numerals have no symbol for zero.
Numbers from 1 to 10 can be written with Roman numerals as I, II, III, IV, V, VI, VII, VIII, IX, X. So, how do we read them?
Any numeral which is repetitive and next to each other are added up, also known as additive notation. Any numeral with greater first and smaller next to greater are added up too, also a additive notation. Any numeral with smaller first and greater next to smaller are subtracted, also known as subtractive notation. Let’s see them in detail.
Additive Notation
With Additive notation, Roman numerals are added up. There are two cases where these numerals are added up.
First case, when Roman numerals are repeated. For example, II, here I is repeated two times. So, the number it makes is 1 + 1 = 2.
Second case, when a greater numeral is followed up by a smaller numeral. For example, VI, here V has value of 5 and I has a value of 1. So, V is greater than I and V is followed by I. Therefore, we can add them up as 5 + 1, which is 6. So, VI is number 6.
Subtractive Notation
With Subtractive notation, Roman numerals are subtracted. When a smaller numeral is followed up by a greater numeral, a smaller numeral is subtracted from a greater numeral. For example, IV, here V has value of 5 and I has a value of 1. So, I is followed by greater numeral V. Therefore, we subtract them as 5 – 1, which is 4. So, IV is a number 4.
Symbols V, L and D are never repeated.
As said above, symbols V, L and D are never repeated, that is why 10 is written as X, not VV. Similarly, 100 is written as C, not LL.
Let’s learn more examples of how to write numerals.
Examples of repetitive numerals
II = 1 + 1 = 2
III = 1 + 1 + 1 = 3
XX = 10 + 10 = 20
XXX = 10 + 10 + 10 = 30
Examples of additive notation
VI = 5 + 1 = 6
XIII = 10 + 1 + 1 + 1 = 13
LXII = 50 + 10 + 1 + 1 = 62
CXV = 100 + 10 + 5 = 115
Examples of subtractive notation
IV = 5 – 1 = 4
IX = 10 – 1 = 9
XL = 50 – 10 = 40
XC = 100 – 10 = 90
CD = 500 – 100 = 400
Examples of additive and subtractive notations
XIV = 10 + (5 – 1) = 10 + 4 = 14
XXXIX = 10 + 10 + 10 + (10 – 1) = 30 + 9 = 39



