Decimal to Roman Numeral Conversion

Objective: Write a program that converts a decimal number (in the range of 1 to 5000) into its equivalent Roman numeral representation. Roman numerals are based on the following symbols:

• • I → 1

• • V → 5

• • X → 10

• • L → 50

• • C → 100

• • D → 500

• • M → 1000

Constraints:

• • The decimal number to be converted will be in the range of 1 to 5000, inclusive.

• • Roman numerals must be represented in their standard form, where symbols are placed from left to right in order of value, starting with the largest. However, to avoid four characters being repeated in succession (such as IIII or XXXX), subtractive notation is used:

     

    • • IV (4), IX (9)
    • • XL (40), XC (90)
    • • CD (400), CM (900)

Input:

• • A single integer, num, where 1 ≤ num ≤ 5000.

Output:

• • A string representing the Roman numeral equivalent of the input number.

Examples:

1. 1. Input: 3 Output: III

1. 1. Input:58Output:LVIII

       

      • • Explanation: L = 50, V = 5, III = 3.

1. 1. Input:1994Output:MCMXCIV

       

      • • Explanation: M = 1000, CM = 900, XC = 90, and IV = 4.

Note: The Roman numeral system does not have a standard representation for zero or negative numbers, and it does not include the concept of decimal fractions. Ensure your solution correctly handles the defined input range and uses the subtractive notation where applicable.

Certainly! Below is a structured approach for writing a blog post that explains how to convert decimal numbers to Roman numerals, complete with tables to illustrate the concept clearly.

Converting Decimal Numbers to Roman Numerals: A Step-by-Step Guide

Roman numerals have fascinated people for centuries with their unique representation and historical significance. Unlike the decimal system, which is based on ten different digits (0 through 9), the Roman numeral system is based on letters from the Latin alphabet to represent numbers. This system is still used today in various contexts, including clock faces, book chapters, and movie sequels. In this guide, we will explore how to convert decimal numbers into Roman numerals, a process that might seem complex at first but is quite straightforward once you understand the basic principles.

Understanding Roman Numerals

The Roman numeral system uses seven basic symbols to represent numbers. Here’s a table of these symbols and their corresponding decimal values:

The Rules of Roman Numerals

There are a few key rules to remember when writing Roman numerals:

1. 1. Repetition: A symbol can be repeated up to three times to add up values. For example, “III” equals 3, and “XX” equals 20.

1. 1. Subtractive Notation: To avoid four characters repeating, subtractive notation is used. This involves placing a smaller numeral before a larger one to indicate subtraction. For example, “IV” represents 4 (5 – 1), and “IX” represents 9 (10 – 1).

1. 1. Descending Order: Roman numerals are written in descending order from left to right, with the largest values first.

Example 1: The Number 276

To write the number 276 in Roman numerals, we break it down into its components based on the largest Roman numeral values that fit:

• 200 is represented by “CC” (100 + 100).
• 70 is represented by “LXX” (50 + 10 + 10).
• 6 is represented by “VI” (5 + 1).

Putting it all together in descending order, we get CCLXXVI.

Example 2: The Number 1994

For the number 1994, we again use the largest values first:

• 1000 is “M”.
• 900 is “CM” (1000 – 100).
• 90 is “XC” (100 – 10).
• 4 is “IV” (5 – 1).

So, 1994 in Roman numerals is MCMXCIV.

Example 3: The Number 444

To convert 444 into Roman numerals:

• 400 is “CD” (500 – 100).
• 40 is “XL” (50 – 10).
• 4 is “IV” (5 – 1).

Thus, 444 in Roman numerals is CDXLIV.

Key Points:

• Descending Order: The examples show how numbers are broken down and represented in Roman numerals, starting with the largest value that fits and proceeding to the smallest.
• Subtractive Notation: When a smaller numeral precedes a larger one, it is subtracted, as seen in “IV” (4), “IX” (9), “XL” (40), “XC” (90), “CD” (400), and “CM” (900).
• Sum of Parts: The final Roman numeral is the sum of its parts, read from left to right, with no numeral repeated more than three times in a row.

By following these guidelines, you can accurately represent any number within the Roman numeral system’s constraints, adhering to its unique syntax and structure.

Example 1: The Number 276

To write the number 276 in Roman numerals, we break it down into its components based on the largest Roman numeral values that fit:

• • 200 is represented by “CC” (100 + 100).

• • 70 is represented by “LXX” (50 + 10 + 10).

• • 6 is represented by “VI” (5 + 1).

Putting it all together in descending order, we get CCLXXVI.

Example 2: The Number 1994

For the number 1994, we again use the largest values first:

• • 1000 is “M”.

• • 900 is “CM” (1000 – 100).

• • 90 is “XC” (100 – 10).

• • 4 is “IV” (5 – 1).

So, 1994 in Roman numerals is MCMXCIV.

Example 3: The Number 444

To convert 444 into Roman numerals:

• • 400 is “CD” (500 – 100).

• • 40 is “XL” (50 – 10).

• • 4 is “IV” (5 – 1).

Thus, 444 in Roman numerals is CDXLIV.

Key Points:

• • Descending Order: The examples show how numbers are broken down and represented in Roman numerals, starting with the largest value that fits and proceeding to the smallest.

• • Subtractive Notation: When a smaller numeral precedes a larger one, it is subtracted, as seen in “IV” (4), “IX” (9), “XL” (40), “XC” (90), “CD” (400), and “CM” (900).

• • Sum of Parts: The final Roman numeral is the sum of its parts, read from left to right, with no numeral repeated more than three times in a row.

By following these guidelines, you can accurately represent any number within the Roman numeral system’s constraints, adhering to its unique syntax and structure.

Step-by-Step Conversion

To convert a decimal number to a Roman numeral, follow these steps:

1. 1. Start with the highest value: Determine the largest Roman numeral value that fits into the decimal number.

1. 1. Subtract and repeat: Subtract this value from your decimal number, then repeat the process with the remainder, working your way down through the Roman numeral values.

1. 1. Use subtractive notation: Apply subtractive notation where necessary to avoid four consecutive symbols.

Here’s a detailed table showing the Roman numeral symbols, their decimal values, and their sequence in the system:

Using these values and rules, you can convert any decimal number into a Roman numeral.

Example Conversion

Let’s convert the decimal number 1994 into a Roman numeral:

1. 1. Start with 1000 (M): 1994 – 1000 = 994.

1. 1. Next, 900 (CM): 994 – 900 = 94.

1. 1. Then, 90 (XC): 94 – 90 = 4.

1. 1. Finally, 4 (IV): 4 – 4 = 0.

The Roman numeral for 1994 is MCMXCIV.

Implementing Decimal to Roman Numeral Conversion in Java

package com.codetechsummit.src.collabera.romannumber;

import java.lang.ref.PhantomReference;
import java.lang.ref.SoftReference;
import java.util.Scanner;

public class DecimalToRoman {
    private static final int[] DECIMAL_VALUES =   {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
    private static final String[] ROMAN_SYMBOLS = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};

    public static String decimalTORomanConversion(int num){
        StringBuilder roman = new StringBuilder();
        for(int i=0; i< DECIMAL_VALUES.length; i++){
            while (num >= DECIMAL_VALUES[i]){
                num-=DECIMAL_VALUES[i];
                roman.append(ROMAN_SYMBOLS[i]);
            }
        }
        return roman.toString();
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int num = scanner.nextInt();
        System.out.println(decimalTORomanConversion(num));
    }
}