Question

Write the following Roman numerals as Arabic numbers. \(\mathrm{XC}\) ______

Short answer

90

Step-by-step solution

Understand Roman Numerals

The first step is to understand what each symbol in a Roman numeral represents. In Roman numerals, - \(X\) stands for 10.- \(C\) stands for 100. Roman numerals are read from left to right.

Apply Subtraction Rule

In Roman numerals, when a smaller number appears before a larger number, you subtract the smaller one from the larger one. Here, \(X\) (10) is before \(C\) (100), so you subtract 10 from 100.

Calculate the Arabic Value

By applying the subtraction rule, \(C\) (100) minus \(X\) (10) equals 90. Therefore, \(XC\) is equal to 90 in Arabic numerals.

Key concepts

Arabic numerals

Arabic numerals are the number system most people use every day, and it consists of the digits 0 through 9. Unlike Roman numerals, which utilize letters such as \(I\), \(V\), \(X\), and others to represent values, Arabic numerals systematically arrange these digits to create all possible numbers. For example, \(90\) is an Arabic numeral composed of the digits \(9\) and \(0\).
Using Arabic numbers within calculations is straightforward because each digit's place value is multiplied by powers of ten (e.g., the number \(234\) consists of \(2\times100 + 3\times10 + 4\times1\)). This makes operations like addition, subtraction, multiplication, and division easy to perform, thanks to a uniform base 10 system.
Although Roman numerals are more historical in nature, understanding how to convert them into Arabic can be helpful in contexts such as reading old manuscripts or numbering things that denote sequence, like book chapters or movie sequels.

subtraction rule

The subtraction rule is a key principle in Roman numerals that allows for more concise number representation. This rule applies when a smaller numeral appears before a larger numeral. The smaller numeral is subtracted from the larger one. For instance, in the numeral \(XC\), \(X\) (which represents 10) is placed before \(C\) (which represents 100). Thus, you subtract 10 from 100.
This rule is also utilized in other numerals such as \(IV\) where \(I\) (1) comes before \(V\) (5), resulting in \(5-1\) or \(4\). Similarly, \(XL\) represents \(40\) because \(X\) (10) is subtracted from \(L\) (50), yielding \(50-10\).
Understanding this rule is crucial for accurate conversion and comprehension of Roman numerals, especially for those lesser-known numbers, as it reduces confusion and prevents misinterpretation.

numerical conversion

Converting numbers from one system to another is a valuable skill, particularly between Roman numerals and Arabic numerals. Conversion involves a series of clear steps.
Firstly, identify the values of each Roman numeral symbol based on their position in the sequence. Next, apply the subtraction rule if needed, which helps determine when to deduct smaller numeral values from the larger ones. In our example \(XC\), recognize that \(X\) precedes \(C\), so you subtract the 10 represented by \(X\) from the 100 of \(C\), resulting in \(90\).
This conversion method helps translate Roman numeral values into easily understandable Arabic numerals. Mastering numerical conversion widens our ability to interpret and utilize historical documents, inscriptions, and traditional contexts accurately.

symbol values

In Roman numerals, each letter symbol has a specific value that contributes to the overall number representation. Knowing these values is the first step in interpreting Roman numerals accurately.
Here's a quick rundown of the basic Roman numeral symbols and their values:

• \(I\) represents 1
• \(V\) stands for 5
• \(X\) equals 10
• \(L\) is 50
• \(C\) represents 100
• \(D\) stands for 500
• \(M\) equals 1000

More complex numbers are built by combining these symbols. When a smaller numeral comes before a larger one, its value is subtracted; otherwise, add the values together. For example, \(XV\) equals \(15\), while \(IV\) equals \(4\).
Understanding these symbol values is foundational for both reading and converting Roman numerals into Arabic numerals, enabling one to navigate between these two number systems efficiently.