Question

Write the following in Hindu – Arabic numerals.
(a) XLIII
(b) LXIX
(c) CXXXV
(d) CCXXII
(e) CCLXXXII
(f) DXIII

Answer 1

Hint: To solve the given question, we will first find out in which form the numbers are given. Then, we will convert this form into numerical form by using the conversions given: I = 1, V = 5, X = 10, L = 50, C = 100 and D = 500. After converting into numerical form, we will convert them into Hindu – Arabic numerals by placing commas at appropriate places.

Complete step by step solution:
Before solving the given question, we must know that the numbers which are given in the question are in Roman Numeric form. In this form, the numbers are represented by the combination of letters from the Latin alphabet. Some of the alphabets used in this system are I, V, X, L, C and D. For converting Roman form to numeric form, we will sue the following conversions: I = 1, V = 5, X = 10, L = 50, C = 100 and D = 500. After converting into numerical form, we will place one comma after every two digits. Now, we will write the Hindu – Arabic numerals of each part.
(a) XLIII – Now, we know that X = 10 and L = 50. As X is ahead of L, the value of XL will be
\[XL=\left( 50-10 \right)=40\]
The value of III = 3. Thus, we have,
\[XLIII=40+3\]
\[\Rightarrow XLIII=43\]
(b) LXIX: Now, we know that X = 10 and L = 50. The value of IX is 9 as I is ahead of X. Thus, we have,
\[LXIX=50+10+9\]
\[\Rightarrow LXIX=69\]
(c) CXXXV: Now, we know that C = 100, X = 10 and V = 5. Thus, we will get,
\[CXXXV=100+3\left( 10 \right)+5\]
\[\Rightarrow CXXXV=100+30+5\]
\[\Rightarrow CXXXV=135\]
(d) CCXXII: Now, we know that C = 100, X = 10 and I = 1. Thus, we will get,
\[CCXXII=2\left( 100 \right)+2\left( 10 \right)+2\left( 1 \right)\]
\[\Rightarrow CCXXII=200+20+2\]
\[\Rightarrow CCXXII=222\]
(e) CCLXXXII: Now, we know that C = 100, L = 50, X = 10 and I = 1. Thus, we will get,
\[CCLXXXII=2\left( 100 \right)+50+3\left( 10 \right)+2\left( 1 \right)\]
\[\Rightarrow CCLXXXII=200+50+30+2\]
\[\Rightarrow CCLXXXII=282\]
(f) DXIII: Now, we know that D = 500, X = 10 and III = 3. Thus, we will get,
\[DXIII=500+10+3\]
\[\Rightarrow DXIII=513\]

Note: Here, we do not need to put the commas after the third digit from the left side because, in each part, the number of digits is less than 4. Another thing to note is that the order in which the alphabets are present matters. Thus, \[IX\ne XI.\] Similarly, \[XL\ne LX.\] When a smaller number is present to the right of the larger number, then we take their difference instead of adding them.