Question

Roman numeral for the greatest three-digit number is
A) IXIXIX
B) CMIXIX
C) CMXCIX
D) CMIIC

Answer 1

Hint: In these types of questions you should be aware of the system of Roman numerals such as the symbols which it is used to represent the systems of numerical notation use these instructions which will help you to get closer to the solution to the question. We can split the given number in the sum of thousands, hundreds, tenths, and ones. So, we can write all these representations of the numbers together and get the Roman numeral for the given number.

Complete step by step answer:
We know that roman numerals are the system of symbols that are used to represent the number of systems in ancient times. Let’s find out how.
So in the Roman numerals system we use some specific symbols which are used to represent some specific numbers such as I represents 1, V represents 5, X represents 10, L represents 50, C represents 100, D represents 500 and at last, M represents 1000 so there is a basic method to find the values of combinations of symbols which is if a symbol is placed after another symbol which represents equal or greater number adds the values of symbols and the symbol placed before symbol which represents the greater number value gets subtracted.
Let’s take the roman numeral CXL to explain this method so in CXL, C represents the greater number as compare to X and L so values of C and XL will add but in the case of XL, L represents the greater number as compare to X, therefore, the subtraction of values will take place i.e. XL = 50 – 10 = 40 since C = 100, therefore, CXL will be equal to 100 + 40 i.e. 140.
The highest three-digit number is 999.
So, if we look at the number given to us, we can split it in that form. So, if we split the number 999, we get,
$999 = 900 + 90 + 9$
It can be written as,
$ \Rightarrow $ $999 = \left( {1000 - 100} \right) + \left( {100 - 10} \right) + \left( {10 - 1} \right)$
Now, if we substitute M for 1000, C for 100, X for 10, and I for 1, then we will get the Roman numeral as,
$ \Rightarrow 999 = (M - C) + (C - X) + (X - I)$
Rewrite the terms after subtraction,
$ \Rightarrow 999 = CM + XC + IX$
Join the terms,
$ \Rightarrow 999 = CMXCIX$

$\therefore $ The roman numeral for the greatest three-digit number is CMXCIX. Hence, option (C) is the correct answer.

Note:
The students might make a mistake in the last step and may write IX for each 9. This is incorrect as we cannot use numerical values in Roman numbers. So, the correct form of writing 999 will be CMXCIX and not IXIXIX.
The trick concept while dealing with problems of this kind is the knowledge of basic information about the roman system. Only Latin alphabets like (I, V, X, L, C, D, and M) are used in the Roman system.
We can also write $999$ as $IM$ which is not given in the options. Here $IM$ is the same as $CMXCIX$.