Question

Write the following Roman numerals in the Hindu-Arabic system.
\[\begin{align}
  & \text{(a) IV} \\
 & \text{(b) IX} \\
 & (c)XII \\
 & (d)XVI \\
 & (e)XXX \\
 & (f)XL \\
 & (g)XXV \\
 & (h)XLI \\
\end{align}\]

Answer 1

Hint: So here in this question we will see the meaning of symbols of Roman numerals in the Hindu-Arabic system is
The value of 1 in Roman numeral is \[I\],
The value of 5 in Roman numeral is \[V\],
The value of 10 in Roman numeral is \[X\],
The value of 50 in Roman numeral is \[L\],
The value of 100 in Roman numeral is \[C\],
The value of 500 in Roman numeral is \[D\],
The value of 1000 in Roman numerals is \[M\].
With the help of these values, we will solve our given question

Complete step-by-step solution:
Let’s start with our given questions
\[\left( a \right)IV\]
As we know the value of 1 in Roman numeral is \[I\] and the value of 5 in Roman numeral is \[V\]so here we will get,
\[\begin{align}
  & \Rightarrow IV\text{ }=\text{ }5-1\text{ }=\text{ }4 \\
 & ~\Rightarrow IV\text{ }=\text{ }4 \\
\end{align}\]
So, the value of \[IV\] in the Hindu-Arabic system is 4.
\[\left( b \right)\text{ }IX\]
As we know the value of 1 in Roman numeral is \[I\] and The value of 10 in Roman numeral is \[X\] so here we will get,
\[\begin{align}
  & ~\Rightarrow IX\text{ }=\text{ }10-1\text{ }=9~ \\
 & \Rightarrow IX\text{ }=\text{ }9 \\
\end{align}\]
So, the value of \[IX\] in the Hindu-Arabic system is 9.

\[\left( c \right)\text{ }XII\]
As we know the value of 1 in Roman numeral is \[I\] and The value of 10 in Roman numeral is \[X\] so here we will get,
\[\begin{align}
  & \Rightarrow XII\text{ }=\text{ }10+1+1\text{ }=\text{ }12 \\
 & \Rightarrow ~XII\text{ }=\text{ }12 \\
\end{align}\]
So, the value of \[XII\] in the Hindu-Arabic system is 12.
\[\left( d \right)\text{ }XVI\]
As we know the value of 1 in Roman numeral is \[I\], the value of 5 in Roman numeral is \[V\] and The value of 10 in Roman numeral is \[X\] so here we will get,
\[\begin{align}
  & \Rightarrow XVI\text{ }=\text{ }10+5+1\text{ }=\text{ }16 \\
 & \Rightarrow ~XVI\text{ }=\text{ }16 \\
\end{align}\]
So, the value of \[XVI\] in the Hindu-Arabic system is 16.
\[\left( e \right)\text{ }XXX\]
As we know the value of 10 in Roman numeral is \[X\] so here we will get,
\[\begin{align}
  & ~\Rightarrow XXX\text{ }=\text{ }10+10+10\text{ }=\text{ }30~ \\
 & \Rightarrow XXX\text{ }=\text{ }30 \\
\end{align}\]
So, the value of \[XXX\] in the Hindu-Arabic system is 30.
\[\left( f \right)\text{ }XL\]
As we know the value of 10 in Roman numeral is \[X\] and the value of 50 in Roman numeral is \[L\] so here we will get,
\[\begin{align}
  & \Rightarrow XL\text{ }=\text{ }50-10\text{ }=\text{ }40 \\
 & \Rightarrow ~XL\text{ }=\text{ }40 \\
\end{align}\]
So, the value of \[XL\] in the Hindu-Arabic system is 40.
\[\left( g \right)\text{ }XXV\]
As we know the value of 5 in Roman numeral is \[V\] and The value of 10 in Roman numeral is \[X\] so here we will get,
\[\begin{align}
  & \Rightarrow XXV\text{ }=\text{ }10+10+5\text{ }=\text{ }25 \\
 & \Rightarrow ~XXV\text{ }=\text{ }25 \\
\end{align}\]
So, the value of \[XXV\] in the Hindu-Arabic system is 25.
\[\left( h \right)\text{ }XLI\]
As we know the value of 10 in Roman numeral is \[X\], the value of 50 in Roman numeral is \[L\] and the value of 1 in Roman numeral is \[I\] so here we will get,
\[\begin{align}
  & \Rightarrow XLI\text{ }=\text{ }50-10+1\text{ }=\text{ }41~ \\
 & \Rightarrow XLI\text{ }=\text{ }41 \\
\end{align}\]
So, the value of \[XVI\] in the Hindu-Arabic system is 41.

Note: A mistake, which can happen in this type of question is when to subtract and when to add, we will explain it with the simple example of $IV\,and\,\, VI$ so here, first of all, we will take $IV$ If a smaller value is placed before a larger one, we subtract instead of adding. For instance, $IV=5-1=4$
And if the larger number is placed before the smaller number then we add them $VI=5+1=6$
Rules for subtraction:
(i). Subtract only powers of ten, such as I, X, or C. Writing VL for 45 is not allowed: write XLV instead.
(ii). Subtract only a single letter from a single numeral. Write VIII for 8, not IIX; 19 is XIX, not IXX.
(iii). Don't subtract a letter from another letter more than ten times greater. This means that you can only subtract I from V or X, and X from L or C, so MIM is illegal