Question

Hindu-Arabic numeral for MCDXVIII is
\[\begin{align}
  & \text{A}.1618 \\
 & \text{B}.1405 \\
 & \text{C}.1418 \\
 & \text{D}.1481 \\
\end{align}\]

Answer 1

Hint: In this question, we are given a roman numeral and we have to find its numeral is Hindu-Arabic form. For this, we will first understand the Roman and Hindu-Arabic numerals and then learn how to convert one into other. At last, we will convert the given Roman numeral to Hindu-Arabic numeral. The Values of Roman numerals that are used are: I represents 1, V represents 5, X represents 10, L represents 50, C represents 100, D represents 500 and M represents 1000.

Complete step by step answer:
Here, we are given a Roman numeral and we have to convert it into Hindu-Arabic numeral.
Before solving our question, let us first understand the rules of writing Roman numerals.
There are a total of seven alphabets which are used to write roman numbers which are I(1), V(5), X(10), L(50), C(100), D(500) and M(1000).
Rule 1: The Roman digits I, X and C are repeated up to three times in succession to form a number. Example: XXX = 10+10+10 = 30. The digits V, L and D are not repeated.
Rule 2: When a digit of lower value is written to the right of higher value, the values of all digits are added. Example: LXV = 50+10+5 = 65.
Rule 3: When a digit of lower value is written to the left of higher value, then the value of lower digit is subtracted from the value of the digit of higher value. Example: XLV = (50-10)+5 = 45. V is never written left to X.
Now, we are given Roman numerals as MCDXVIII here, we can see the three I's at right, so they make up the value 1+1+1 = 3. V is higher than 1 and written to the left of lower value, therefore it will be added to 3, hence VIII becomes 5+3 = 8. X is higher than V and written to the left of lower value, therefore it will be added to 8, hence XVII becomes 10+8 = 18. Now, we can see, C is written left to D but C is smaller value, so it will be subtracted from D. Therefore, CD = 500-100 = 400. But CD is higher than XVII and at left, so it will be added to XVIII. Hence, we get CDXVIII as 400+18 = 418. At last, M is higher value left to CDXVIII so it will be added. Hence, we get MCDXVIII as 1000+418 = 1418.
Hence, Hindu Arabic numeral for MCDXVIII becomes 1418.

So, the correct answer is “Option C”.

Note: Students should be careful while solving these numerals. Rules should be followed carefully. Take care while adding or subtracting the values. Students should note that sometimes V, L and D cannot be repeated and L, X, C can be repeated only three times. For example, while writing 30 we use XXX but for writing 40 we cannot use XXXX but we have to subtract 10 from 50 by using XL.