## Arithmetic Chapter 4 Roman Numbers Up To One Hundred

**Arithmetic Chapter 4 Introduction To Roman Numbers**

1. Among all the human civilizations which have been developed in different terminals of the world, Roman civilization is one of the distinguishable civilizations.

2. From ancient times the Romans are prospering in knowledge science.

3. They are also very experts in mathematical accounts.

4. The signs and symbols which the Romans used to express the numbers are called the Romans’ Number System.

5. The learned people thought that the Roman Numbers originated from the fingers of the hands of the people and from the formation of the hands of the people.

6. For example, the numbers I, II, III, etc. are invented from the formation of the fingers of hands, and the numbers V, X, etc. are also invented from the formation of hands.

7. These are very ancient, and still we use these Roman Numbers abundantly today.

8. We use Roman Numbers in the dial of a clock, for writing the classes of an educational institution, for writing the chapters of a printed book, etc.

9. There are some remarkable number systems other than the Roman Number System.

**For example:**

1. Hindu Arabic Numbers System.

2. Binary numbers system.

1. Hindu Arabic Numbers System.

1. We are also well-known for this system excessively.

2. Generally, we use this system in our mathematical calculations.

3. At present this system is accepted universally and used internationally system.

4. The number of principal signs or symbols in this system is ten such as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

5. Any number (however large or small) can be expressed using these ten symbols one or more times.

6. These signs or symbols are called digits.

2. Binary number system.

1. In this system, any number can be expressed by only two numbers 0 and 1.

## Arithmetic Chapter 4 The Principal Sings or Symbols Of Roman Numbers

1. The number of main alphabets of signs which are used to represent the numbers in Roman numerals is seven such as V, X, L, C, D, M.

2. Using these 7 symbols any number can be expressed in this system.

3. In comparison to the Hindu Arabic Number system, the values of 7 symbols are given in the following table

## Arithmetic Chapter 4 Rules For Writing Roman Numbers

**We can write according to the values of the alphabetical symbols of Roman Numbers:**

1. I<V<X<L<C<D<M

2. So the value of any symbol is always less than that of any symbol on its right side and is always greater than that of any symbol on its left side.

3. If we take two symbols V and C, between these two V is less than C and C is greater than V.

4. This is because C lies on the right side of V.

5. For the same reason between X and D, X is smaller than D and D is greater than X.

**There are some rules for writing Roman Numbers. Now we shall discuss these rules:**

** Rule 1**:

1. In Roman Numbers only I, X, C, and M signs are repeated consecutively not more than 3 times.

2. They can be repeated a maximum of 3 times only, V, L, and D can not be used in any number consecutively more than once.

3. We can not use 1 four times to write 4 as IIII.

4. To write 40, X cannot be used 4 times as XXXX.

5. To write 600, C can not be used 6 times as CCCCCC.

- We can use I as II, III.
- X as XX, XXX.
- C as CC, CCC.
- M as MM, MMM.
- II = 1 + 1 = 2.
- III= 1 + 1 + 1 = 3.
- XX = 10 + 10 = 20.
- XXX =10 + 10 + 10 = 30.
- CC = 100 + 100 = 200.
- CCC = 100 + 100 + 100 = 300.
- MM = 1000 + 1000 = 2000.
- MMM = 1000 + 1000 + 1000 = 3000.

**
Rule **2:

1. In the Roman Number System, if a sign is repeated in any number, it implies addition.

- II = 1 + 1 = 2.
- III = 1 + 1 + 1 + 3.
- XX = 10 + 10 = 20.
- XXX = 10 + 10 + 10 = 30.
- CC = 100 + 100 = 200.
- CCC = 100 + 100 + 100 = 300.
- MM = 1000 + 1000 = 2000.
- MMM = 1000 + 1000 + 1000 = 3000.

** Rule 3**:

1. In the Roman Number System, if a number is expressed when a sign of a smaller value is inserted after a sign of greater value then the value of the number will be the sum of the values of the signs.

2. For example, suppose a number is expressed as VI, then the value of the sign (or symbol) V is greater than the value of the sign (or symbol) I i.e., here a sign of smaller value is placed after a sign of greater value.

- The value of the number which is expressed as VI = 5 + 1 = 6
- Similarly, XII = 10 + 1 + 1 = 12,
- LIII = 50 + 1 + 1 + 1 = 53, .
- LXXV = 50 + 10 + 10 + 5 = 75,
- LXXXI = 50 + 10 + 10 + 10 + 1 = 81

** Rule 4**:

1. In the Roman Number System, if a number is expressed when a sign of smaller value is inserted before a sign of greater value, then the value of the number will be the difference between the values of the Signs (here the smaller value of the sign is subtracted from the greater value of the sign).

2. For example, suppose a number is expressed by IV. In this number, the value of the sign V is greater than the value of the sign I, and the sign I is placed on the left side of V.

- So the value of the number which is expressed as IV = 5 – 1 = 4.
- Similarly, IX = 10 – 1 = 9.
- XL = 50 – 10 = 40.
- CD = 500 – 100 = 400 etc.

:

Rule 5

1. If a sign (or symbol) of smaller value is placed between the two signs of greater values, then the value of the sign of smaller value is subtracted from the greater value of the next sign to be placed and never be added to the greater value of sign which is placed before the sign of smaller value.

2. For example, suppose a number is expressed by Roman Number System XIV.

3. Here the sign I of smaller value is placed between two signs X and V of greater values.

4. So according to the rule, the value of I is subtracted from the value of V (v V is the sign of greater value which is placed next to I) and the value of the number will be (XIV)

= 10 + (5 – 1)

= 14

- Similarly, X3X = 10 + (10 – 1) = 10 + 9 = 19.
- LXL = 50 + (50 – 10) = 50 + 40 = 90.
- CXC = 100 + (100 – 10) = 100 + 90 = 190.
- DCD = 500 + (500 – 100) = 500 + 400 = 900.
- DCM = 500 + (1000 – 100) = 500 + 900 = 1400.
- MCD = 1000 + (500 – 100) = 1000 + 400 = 1400.
- MCM = 1000 + (1000 – 100) = 1000 + 900 = 1900.
- MCDLX = 1000 + (500 – 100) + 50 + 10 = 1000 + 400 + 50 + 10 = 1460.
- MCMLX = 1000 + (1000 – 100) + 50 + 10 = I960.

**Rule 6:**

1. To mean one thousand times any number or of the value of any sign, a small line above the sign is drawn.

2. For example, 1000 times of X = X = X x 1000 = 10 x 1000 = 10000.

- In the same way, we have,
- C = C x 1000 = 100 x 1000 = 100000.
- M = M x 1000 = 100 x 1000 = 1000000.
- XXTV = XXIV x 1000 = [10 + 10 + (5 – 1)] x 100 = 24 x 1000 = 24000.

## Arithmetic Chapter 4 Characteristics Of The Roman Number System

1. There is no sign to express zero in the Roman Number System.

2. The same number can be arranged in different ways.

3. For Example 1400 = DCM ; 1400 = MCD

4. In the Roman Number System, the difference in the values of any two consecutive signs of the main 7 alphabetic signs is not fixed.

5. For example,

- The difference between the values of I and V = 5 – 1 = 4.
- The difference between the values of V and X = 10 – 5 = 5.
- The difference between the values of X and L = 50 – 10 = 40.
- The difference between the values of L and C = 100 – 50 = 50,
- The difference between the values of C and D = 500 – 100 = 400,
- The difference of the values of D and M = 1000 – 500 = 500.

6. On the other hand, in Hindu Arabic Number System, the difference between 0 and 1 = 1— 0=1

- The difference of 1 and 2 = 2 — 1 = 1
- The difference of 2 and 3 = 3 – 2 = 1
- The difference of 8 and 9 = 9 — 8= 1

7. ∴ The difference between two consecutive numbers is always the same 1.