Question

The number obtained when 144 is divided by 16 in roman number
(a) \[\text{X}\]
(b) \[\text{VII}\]
(c) \[\text{VIII}\]
(d) \[\text{IX}\]

Answer 1

Hint: In this type of question we have to use the concept of roman numerals conversion. In conversion of a number into Roman numeral 7 major letters are used they are \[\text{I,V,X,L,C,D }\!\!\And\!\!\text{ M}\] used to denote the numbers 1, 5, 10, 50, 100, 500 & 1000 respectively. Roman letters are usually written largest to smallest from left to right but not always. When we write Roman letters largest to smallest from left to right a letter to the right of another letter then it get added, for example when we write a Roman number \[\text{XVIII}\] then it will represent a number 18 as \[\text{XVIII = 10+5+3 = 18}\]. Also when we write Roman letters smallest to largest from left to right a letter to the left of another letter then it gets subtracted, for example \[\text{CD}\] then it will represent a number 400 as \[\text{CD = 500 - 100 = 400}\]. Now, here first we perform the division of 144 and 16 then the quotient obtained we write it in Roman numerals.

Complete step-by-step solution:
Now, we have to express the number obtained when 144 is divided by 16 in Roman numerals.
For this let us first perform division of 144 and 16
\[\Rightarrow 16\overset{9}{\overline{\left){\begin{align}
  & 144 \\
 & \underline {- 144} \\
 &0 \\
\end{align}}\right.}}\]
Hence, when we divide 144 by 16 we get 9. Now we have to express 9 in Roman numerals.
Now, we know that we can express 9 as \[9=10-1\] and hence in roman numerals we can write the number 9 as \[\text{IX}\]
Hence, option (d) is the correct option.

Note: In this type of question we have to note that Roman numerals are special characters and alphabets that represent a number using lines and letters. Also students have to remember that in case of Roman numerals we cannot use the \[\text{IIII}\] instead of that we use the subtraction principle. A subtraction notation is used in the case of 400, 900, 40, 90, 9 and 4 to differentiate between the existing digits.