# Decimal to Roman Converter

## Converting a Decimal Number to Roman Numerals

Roman numerals are a numeral system that originated in ancient Rome and were widely used throughout Europe until the Late Middle Ages. Unlike the modern decimal system (base 10), Roman numerals are non-positional and do not have a zero. Instead, they rely on combinations of letters from the Latin alphabet to represent values.

The Roman numeral system uses the following basic symbols:

- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000

To convert a decimal number to Roman numerals, the following rules apply:

- **Addition Rule**: If a smaller numeral follows a larger numeral, the values are added. For example, VI = 5 + 1 = 6.
- **Subtraction Rule**: If a smaller numeral precedes a larger numeral, the smaller value is subtracted from the larger. For example, IV = 5 - 1 = 4.
- **Repetition Rule**: The numerals I, X, C, and M can be repeated up to three times in succession to form numbers. For example, III = 3 and XXX = 30.
- **Non-Repetition Rule**: The numerals V, L, and D cannot be repeated. Instead, combinations like IX (9) and XL (40) are used.
- **Largest to Smallest Rule**: Roman numerals are written from largest to smallest, starting from the left. For example, in the number 2021 (MMXXI), M (1000) comes before X (10), and X comes before I (1).

## Examples

Let’s go through some examples to understand how to convert decimal numbers to their Roman numeral equivalents. In each example, we'll break down the number step by step and apply the appropriate Roman numeral conversion rules.

### 1. Convert the decimal number 149 to Roman numerals.

#### Answer

First, we identify the given number:

**Given:**

- Decimal: 149

To convert 149 to Roman numerals, we start by breaking it down according to the place values:

**Steps:**

- 149 consists of 100 (C), 40 (XL), and 9 (IX).
- We apply the subtraction rule for 40 and 9 because 40 is formed by placing X before L (XL), and 9 is formed by placing I before X (IX).
- Thus, 149 in Roman numerals is represented as C (100) + XL (40) + IX (9).

The final Roman numeral is formed by concatenating these symbols:

**Roman Numeral Equivalent:**

CXLIX

**Result:**

∴ The Roman numeral equivalent of the decimal number 149 is CXLIX.

### 2. Convert the decimal number 58 to Roman numerals.

#### Answer

We start by identifying the number:

**Given:**

- Decimal: 58

Next, we break down the number using the Roman numeral system:

**Steps:**

- 58 consists of 50 (L) and 8 (VIII).
- We apply the addition rule for 8, as it is formed by adding I three times after V (VIII = 5 + 3 = 8).
- Thus, 58 in Roman numerals is represented as L (50) + VIII (8).

The final Roman numeral is formed by concatenating these symbols:

**Roman Numeral Equivalent:**

LVIII

**Result:**

∴ The Roman numeral equivalent of the decimal number 58 is LVIII.

### 3. Determine the Roman numeral equivalent of the decimal number 2021.

#### Answer

First, we identify the given number:

**Given:**

- Decimal: 2021

Next, we break down the number using the Roman numeral system:

**Steps:**

- 2021 consists of 2000 (MM), 20 (XX), and 1 (I).
- We apply the repetition rule for M (1000) to represent 2000 (MM).
- We apply the addition rule for 20, as it is formed by adding X twice (XX = 10 + 10 = 20).
- Thus, 2021 in Roman numerals is represented as MM (2000) + XX (20) + I (1).

The final Roman numeral is formed by concatenating these symbols:

**Roman Numeral Equivalent:**

MMXXI

**Result:**

∴ The Roman numeral equivalent of the decimal number 2021 is MMXXI.

### 4. Convert the decimal number 3999 to Roman numerals.

#### Answer

We start by identifying the number:

**Given:**

- Decimal: 3999

Next, we break down the number using the Roman numeral system:

**Steps:**

- 3999 consists of 3000 (MMM), 900 (CM), 90 (XC), and 9 (IX).
- We apply the repetition rule for M (1000) to represent 3000 (MMM).
- We apply the subtraction rule for 900, 90, and 9 because these numbers are formed by placing a smaller numeral before a larger one (CM = 1000 - 100, XC = 100 - 10, IX = 10 - 1).
- Thus, 3999 in Roman numerals is represented as MMM (3000) + CM (900) + XC (90) + IX (9).

The final Roman numeral is formed by concatenating these symbols:

**Roman Numeral Equivalent:**

MMMCMXCIX

**Result:**

∴ The Roman numeral equivalent of the decimal number 3999 is MMMCMXCIX.