Roman Numerals Conversion

Introduction

In the Middle Ages, the roman number system is considered a standard writing system for numbers throughout Europe. Romans invented it for daily life because they could not count more than ten using their fingers. Latin numbers are the words in Latin that are used to count numbers. They are also represented by roman numerals but are read in Latin. Roman numbers consist of symbols containing alphabets as some base numbers.

Numbers

Numbers play a huge part in daily life and mathematics. They are used to counting things, without numbers it is tough to count and remember the number of things. Numbers are also used to measure things, and arithmetic operations are possible because of numbers. Numbers can be represented in words like 1 → one, 2 → two, etc… There are different types of numbers. Every number is derived from these ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Counting things starts from one and goes on as much as possible till infinity. Zero represents none in mathematics it is the value of nothing.

There are many types of numbers in mathematics −

• Natural Numbers − The positive integers which are used in counting start from one and go to infinity. Denoted by “N”. Example − 1, 2, 3, 4.....

• Whole Numbers − The non-negative integers, are a union of zero and natural numbers. Denoted by “W”. Example − 0, 1, 2, 3, 4.....

• Integers − Integers are a union of whole numbers and negative natural numbers. Denoted by “Z”. Example − -3, -2, 0, 1, 2, ......

• Rational Numbers − The numbers which can be written in $\mathrm{\frac{p}{q}\:,\:q\:\neq\:0}$ the form. It includes decimal numbers. Denoted by “Q”. Example − $\mathrm{2\:,\:\frac{1}{2}\:,\:\frac{3}{4}\:,\:}$, etc…

• Irrational Numbers − The numbers which cannot be written in $\mathrm{\frac{p}{q}\:,\:q\:\neq\:0}$ the form. Denoted by “P”. Example − $\mathrm{\sqrt{2}\:,\:\sqrt{3}\:,}$ etc…

• Real Numbers − All types of numbers without imaginary numbers are real numbers. denoted by “R”. Example − 1, 2, −3, etc…

• Complex Numbers − The numbers in the form of a + bi, where a, and b are real numbers. i is the imaginary number. Denoted by “C”. Example − $\mathrm{3\:+\:5i\:,\:4\:+\:6i\:,}$ etc…

• Imaginary Numbers − The numbers which are the product of a real number and imaginary number “i”. Example − $\mathrm{2i\:,\:5i\:,}$ etc…

There are some other types of numbers divided among themselves

• Even Numbers − The numbers when divided by 2 give a remainder of zero are called even numbers. Example − 2, -6, 14, 56, etc…

• Odd Numbers − The numbers when divided by 2 give a remainder of one are called odd numbers. Example − 1, -5, 13, 37, etc…

Roman Numerals

Roman numerals are an ancient number system used by Romans. It contains a few letters as base numbers from which the other numbers are derived. The most common letters used to represent Roman numerals are I, V, X, L, C, D, and M. They also represent years.

The values of these letters are listed in the below table.

I	V	X	L	C	D	M
1	5	10	50	100	500	1000

The below table contains roman numerals representing 1 to 10 numbers.

I	II	III	IV	V	VI	VII	VIII	IX	X
1	2	3	4	5	6	7	8	9	10

The below table contains roman numerals representing 10 multiples up to 100.

X	XX	XXX	XL	L	LX	LXX	LXXX	XC	C
10	20	30	40	50	60	70	80	90	100

The below table contains roman numerals representing 100 multiples up to 1000.

C	CC	CCC	CD	D	DC	DCC	DCCC	CM	M
100	200	300	400	500	600	700	800	900	1000

Rules for writing Roman numerals using the letters:

• If a letter with a lower value is written left of a symbol with a higher value then it is subtracted. Example − $\mathrm{IV\:=\:5\:-\:1\:=\:4}$.

• If a letter with a lower value is written right of a symbol with a higher value then it is added. Example − $\mathrm{VI\:=\:5\:+\:1\:=\:6}$.

• Only the letters I, X and C are used as numerals which can be subtracted when placed left of a higher value.

• The letters L, V, and D cannot be repeated, if so the number is invalid. Only the letters I, X, and C can be repeated in a row thrice in a number.

• If a letter is placed in succession it is added to itself. Example − $\mathrm{II\:=\:1\:+\:1\:=\:2}$. It can be repeated in succession a maximum of three times.

• L, V, and D are never subtracted because they are never placed left of a higher value letter. I can be subtracted only from V, X. X can be subtracted only from L, M, and C only.

Conversion Between Roman Numerals and Latin Numerals

The below table consists of roman numerals in Latin.

I	II	III	IV	V	VI	VII	VIII	IX	X
unus	duo	tres	quattour	quinque	sex	septem	octo	novem	decem

Solved Examples

Write 1765 in roman numeral form?

$\mathrm{1765\:=\:1000\:+\:700\:+\:60\:+\:5}$

$\mathrm{1000\:=\:M}$

$\mathrm{700\:=\:DCC}$

$\mathrm{60\:=\:LX}$

$\mathrm{5\:=\:V}$

$\mathrm{1765\:=\:MDCCLXV}$

2) Calculate the value of the roman numeral $\mathrm{DXLI\:-\:CLIV}$ ?

The value of $\mathrm{DXLI\:=\:541\:;\:CLIV\:=\:154}$

Substitute the values $\mathrm{DXLI\:-\:CLIV\:=\:541\:-\:154\:=\:387}$

$\mathrm{387\:=\:300\:+\:80\:+\:7}$

$\mathrm{300\:=\:CCC\:;\:80\:=\:LXXX\:;\:7\:=\:VII}$

$\mathrm{387\:=\:CCCLAAAVII}$

$\mathrm{DXLI\:-\:CLIV\:=\:CCCLXXXVII}$

Conclusion

In this tutorial, we learned about numbers, different types of numbers, roman numerals, rules to write roman numerals, conversion between roman numerals, and Latin numerals, and a few solved examples on writing roman numerals.

FAQs

1. Write 27 in roman numeral form?

$\mathrm{27\:=\:20\:+\:7\:=\:20\:+\:5\:+\:2}$

$\mathrm{20\:=\:XX\:;\:5\:=\:V\:;\:2\:=\:II}$

$\mathrm{27\:=\:XXVII}$

2. Write 59 in roman numeral form?

$\mathrm{59\:=\:50\:+\:9\:=\:50\:+\:10\:-\:1}$

$\mathrm{50\:=\:L\:;\:10\:=\:X\:;\:1\:=\:I}$

$\mathrm{59\:=\:LIX}$

3. Write 78 in roman numeral form?

$\mathrm{78\:=\:70\:+\:8\:=\:70\:+\:10\:-\:2}$

$\mathrm{70\:=\:LXX\:;\:10\:=\:X\:;\:2\:=\:II}$

$\mathrm{78\:=\:LXXXII}$

4. Write 1438 in roman numeral form?

$\mathrm{1438\:=\:1000\:+\:400\:+\:30\:+\:8}$

$\mathrm{1000\:=\:M}$

$\mathrm{400\:=\:CD}$

$\mathrm{30\:=\:XXX}$

$\mathrm{8\:=\:VIII}$

$\mathrm{1438\:=\:MCDXXXVIII}$

5. Difference between odd and even numbers?

Even Numbers − The numbers when divided by 2 give a remainder of zero are called even numbers. Example − 12, -16, 4, 6, etc…

Odd Numbers − The numbers when divided by 2 give a remainder of one are called odd numbers. Example − 11, -15, 1, 23, etc…