Question

Write the following Arabic numbers as Roman numerals. \(30\) ______

Short answer

30 is written as XXX in Roman numerals.

Step-by-step solution

Understand Roman Numerals

Roman numerals are represented by combinations of letters from the Latin alphabet. The most basic Roman numerals are I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). To write numbers, these letters are combined in various ways. Smaller numbers before larger ones mean subtraction, whereas larger or same sized numbers are added if placed consecutively.

Break Down the Number

The given number is 30. To represent this using Roman numerals, we need to express it as a combination of the basic Roman numeral values. Since the nearest basic value smaller than 30 is 10 (represented by X), we can express 30 using multiple X's.

Construct the Roman Numeral

To write 30 as a Roman numeral, simply write three X's: XXX. This is because each X represents 10, and three of them added together (X + X + X) equals 30.

Key concepts

Arabic Numbers

Arabic numbers, also known as Hindu-Arabic numerals, are the ten digits commonly used worldwide: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These numerals form the basis of the decimal system. They are named to honor the Indian mathematicians who developed them and the Arab scholars who introduced them to Europe. Our daily math and counting rely on these Arabic numbers. We write numbers using these digits arranged in sequences, with each place representing a different power of ten. For example:

• The number 30 is written using two digits: a 3 in the tens place, indicating three groups of ten, and a 0 in the units place, indicating no additional ones.
• They have a widespread use in mathematical operations and financial transactions.

These numbers provide a straightforward way to represent all sorts of quantities and calculations.

Latin Alphabet

The Latin alphabet is a set of letters that forms the foundation of the Roman numeral system. Originating from ancient Rome, this alphabet includes the standard letters that many languages worldwide use today, including English. However, in Roman numerals, only a select few letters are used. Roman numerals utilize the following letters from the Latin alphabet:

• I
• V
• X
• L
• C
• D
• M

Each letter serves as a symbol for a specific number, rather than a sound, as in typical alphabetical use. Learning these letters is key to understanding how Roman numerals work.

Number Representation

Number representation in Roman numerals is a bit different from the Arabic numeral system. Instead of using place value to determine the number, Roman numerals combine symbols to represent it. Key features of Roman number representation include:

• Symbols are combined to create numbers, often adding or subtracting values from each other.
• Placing a smaller numeral before a larger one indicates that the smaller number should be subtracted.
• Conversely, when numerals are listed in descending order or identical numbers are grouped, their values are added.

So, to express number 30, Romans would use three X's (XXX), since each X equals 10. Adding them gives us the total of 30.

Basic Roman Numeral Values

Basic Roman numeral values are fundamental to understanding and composing Roman numbers. Each numeral signifies a specific value, and by knowing these, you can easily decode or create numbers in the Roman format. The primary Roman numerals and their corresponding values are:

• I for 1
• V for 5
• X for 10
• L for 50
• C for 100
• D for 500
• M for 1000

Each of these can be combined with others to represent a wide range of numbers. Understanding these basic values makes it easier to convert between Arabic numbers and Roman numerals. For example, the representation of 30 is straightforward: by repeating the numeral X three times, we reflect its value multiplicatively (X + X + X).