Unit, Number, Numeral & Number System

What is Unit?

Everywhere in our daily life we come across hearing or visualising 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 we see in counting things? It is the number always e.g. 6 or 12 or 2 etc. and what is the type of thing we are counting like pen, banana, bike.

Let’s take another example to know it better, there are 5 pears in a basket. So, here we have thing to be counted is pear. One pear or a pear is a single thing we can think of, which is also called as 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 as number. So, a number is “how many times a unit is taken”. By definition, a unit is something that denotes a single thing.

Example

A pen, a girl, a day etc.

So, here a pen is a single thing, which is a unit.

What is Number?

As explained above, 5 pears denote a unit is taken 5 times. Here, unit is a pear and it is taken as 5 in numbers. By definition, a number denotes how many times a unit is taken.

Example

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, 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, unit is a day which is a and single thing.

How many times the days are taken i.e. 7 times. So, 7 is a number.

This is how unit and number are useful to represent any quantity of any thing.

What is Numeral?

We learnt about 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.

Example

Four is represented by the symbol 4 which is a numeral.

What are the Numeral Systems?

A numeral systems are the systems 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

Hindu Arabic Numeral System is the most adapted system in the world to represent a number. This system was invented by Indian mathematicians between 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.

Hindu Arabic Numeral symbols
Hindu Arabic Numeral symbols

Hindu Arabic numerals upto 100

Numeral
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Numeral
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Numeral
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Numeral
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Numeral
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100

Roman Numeral 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.

Roman symbols
Roman symbols

How to write a number with Roman numerals?

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 is when Roman numerals are repeated. For example, II, here I is repeated two times. So, the number it makes is 1 + 1 = 2.

Second is when 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 a number 6.

Subtractive Notation

With Subtractive notation, Roman numerals are subtracted. When smaller numeral is followed up by a greater numeral, smaller numeral is subtracted from 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.

Note

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.

Example

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 = 72

CXV = 100 + 10 + 5 = 115


Examples of subtractive notation

IV = 5 – 1 = 4

IX = 10 – 1 = 9

XL = 50 – 10 = 60

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

Roman numerals upto 100

Roman Value
I1
II2
III3
IV4
V5
VI6
VII7
VIII8
IX9
X10
XI11
XII12
XIII13
XIV14
XV15
XVI16
XVII17
XVIII18
XIX19
XX20
XXI21
XXII22
XXIII23
XXIV24
XXV25
Roman Value
XXVI26
XXVII27
XXVIII28
XXIX29
XXX30
XXXI31
XXXII32
XXXIII33
XXXIV34
XXXV35
XXXVI36
XXXVII37
XXXVIII38
XXXIX39
XL40
XLI41
XLII42
XLIII43
XLIV44
XLV45
XLVI46
XLVII47
XLVIII48
XLIX49
L50
Roman Value
LI51
LII52
LIII53
LIV54
LV55
LVI56
LVII57
LVIII58
LVIX59
LX60
LXI61
LXII62
LXIII63
LXIV64
LXV65
LXVI66
LXVII67
LXVIII68
LXIX69
LXX70
LXXI71
LXXII72
LXXIII73
LXXIV74
LXXV75
Roman Value
LXXVI76
LXXVII77
LXXVIII78
LXXIX79
LXXX80
LXXXI81
LXXXII82
LXXXIII83
LXXXIV84
LXXXV85
LXXXVI86
LXXXVII87
LXXXVIII88
LXXXIX89
XC90
XCI91
XCII92
XCIII93
XCIV94
XCV95
XCVI96
XCVII97
XCVIII98
XCIX99
C100