Question

Write the following Arabic numbers as Roman numerals. \(12\) ______

Short answer

The Roman numeral for 12 is XII.

Step-by-step solution

Understand the Roman Numeral Symbols

Familiarize yourself with the basic Roman numeral symbols and their respective values. The main symbols we need are: \(I = 1\), \(V = 5\), \(X = 10\), \(L = 50\), \(C = 100\), \(D = 500\), and \(M = 1000\).

Breakdown the Number

Break down the Arabic number 12 into its components using Roman numeral values. We can express 12 using the symbols we learned: \(X = 10\) to cover the tens, and then we need \(2\) more, which is \(II = 2\).

Convert to Roman Numerals

Combine the Roman numerals corresponding to the parts: starting with \(X\) for ten and adding \(II\) for two. Hence, the combination for 12 is \(XII\).

Key concepts

Arabic Numbers

Arabic numbers, also known as Hindu-Arabic numerals, are the ten digits we commonly use today: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These numbers form the basis of our counting system and are used worldwide in daily life, mathematics, commerce, and more. Their invention is attributed to Indian mathematicians and was later transmitted to the Western world by Arab scholars. This is why they are often referred to as Arabic numbers.

What makes Arabic numbers particularly useful is their positional nature. The placement of a digit within a number determines its value due to the decimal system based on powers of 10. For example, in the number 12, the digit '1' is in the tens place, making its value 10, while '2' is in the ones place, maintaining its value of 2. This simple yet powerful system makes performing arithmetic operations seamless and intuitive.

Apart from basic arithmetic, Arabic numbers make it easy to express large numbers and fractions, which is a distinct advantage over other numeral systems like Roman numerals. Their simplicity in form and functionality is why Arabic numbers have become the standard numeral system across the globe.

Roman Numeral Conversion

Roman numerals are a numeral system that originated in ancient Rome, using combinations of letters from the Latin alphabet to signify values. Converting between Arabic numbers and Roman numerals can seem daunting, but it becomes manageable once you break it down into smaller steps.

To perform a Roman numeral conversion, you need to know the basic symbols and their values. Common Roman numerals include:

• \(I = 1\)
• \(V = 5\)
• \(X = 10\)
• \(L = 50\)
• \(C = 100\)
• \(D = 500\)
• \(M = 1000\)

The process involves breaking the Arabic number into parts that these symbols can easily express. For example, to convert 12 to Roman numerals, you start with the largest symbol value possible, which is \(X\) for 10. Then, you add the next required value, \(II\) for 2, giving you \(XII\) for 12.

When dealing with larger numbers or those requiring subtraction, such as 4 or 9, the numeral system employs a subtractive notation. For example, 4 is represented as \(IV\), not \(IIII\), and 9 is \(IX\), not \(VIIII\). This approach simplifies numbers and maintains a concise format.

With practice, converting between Arabic numbers and Roman numerals becomes a straightforward task.

Basic Roman Numeral Symbols

Roman numerals rely on a limited set of symbols, each associated with a specific value. Unlike Arabic numbers, which use ten distinct digits, Roman numerals use seven primary symbols. By understanding these symbols and their respective values, one can form any number. The basic Roman numeral symbols are as follows:

• \(I = 1\)
• \(V = 5\)
• \(X = 10\)
• \(L = 50\)
• \(C = 100\)
• \(D = 500\)
• \(M = 1000\)

Using these symbols, Roman numerals are constructed by combining them. The placement in sequence determines the overall numeric value. Generally, Roman numerals are written from largest to smallest, adding up the values to get the final number. For example, in the numeral \(XVII\), you have \(X = 10\), \(V = 5\), and \(II = 2\), which adds up to 17.

To form numbers like 4 or 9, which are not naturally represented on this list, the Roman numeral system uses subtractive combinations. Thus, 4 is \(IV\) (one before five) and 9 is \(IX\) (one before ten). This method maintains fewer symbols while still representing the same value.

Familiarity with these basic symbols is key to understanding and composing Roman numerals for any given number.