CDXLVIII in Roman Numerals

Ancient Romans discovered that counting fingers could get very complicated after 10. So to overcome the complexity, the Roman numeric system was developed. This was widely used throughout Europe as a standard writing system until the late Middle Ages.

Seven symbols are used to represent numbers in the Roman numeric system — I, V, X, L, C, D, and M. The numerals are made up of different combinations of these symbols. CDXLVIII in Roman numerals can be written in number form by adding or subtracting the values of each Roman numeral, i.e. CDXLVIII = 448.

Let us learn more about the Roman numeral CDXLVIII, how we write them, the mistakes we usually make, and ways to avoid these mistakes.

When writing Roman numerals, there are a few rules that we need to follow based on the Roman numerals we are trying to write. In this section, we will learn about the rules when writing Roman numerals and how to represent them.

Rule 1: Addition Method:

When a larger symbol is followed by a smaller symbol, we add the numerals to each other. For example, in VIII, we have 5 + 3 = 8.

Rule 2: Repetition Method:

A symbol that is repeated three times in continuation increases the value of the numeral. For example, XXX = 30.

Rule 3: Subtraction Method:

We use the subtraction method when a larger symbol follows a smaller symbol. For example, XL = 40 (which is 50 – 10).

Rule 4: Limitation Rule:

Symbols cannot be repeated more than three times, and some symbols, such as V, L, and D cannot be repeated more than once. For example, 10 is represented as X and not VV.

Let us learn about how to write CDXLVIII in Roman numerals. There are two methods that we can use to write Roman numerals:

• By Expansion Method

By Grouping Method

The breaking down of Roman numerals into parts and then converting them into numerals is what we call the expansion method. The expansion method is the breaking down of Roman numerals into numerical form and adding them to get the final number.

Step 1: Break the Roman numerals into parts.

Step 2: Now write each of the Roman numerals with its numerical digit in the place value.

Step 3: Add or subtract the numerals accordingly.

For CDXLVIII,

Step 1: First we break the Roman numerals. CDXLVIII = C + D + XL + V + I + I + I

Step 2: Write the Roman Numerals for each part The Roman Numeral C is 100 The Roman Numeral D is 500 The Roman Numeral XL is 40 The Roman Numeral V is 5 The Roman Numeral I is 1

Step 3: Combine all the numbers D (500) - C (100) + XL (40) + V (5) + I (1) + I (1) + I (1) = 448. Therefore, the Roman Numeral CDXLVIII is 448.

Using subtraction and addition rules, we will apply the grouping method. This means we break the Roman numerals into smaller groups, which makes it easier to work with. This method groups the Roman numerals logically, and then we write the numbers for each group.

Step 1: Take the largest number and write the number for that Roman numeral.

Step 2: Write the Roman numeral using the subtraction and addition rules

Example: Let’s take the Roman numeral CDXLVIII.

Step 1: The larger Roman numerals are what we will begin with. Once split, the Roman numerals we get are CD, XL, and VIII. The numeral for CD is 400 The numeral for XL is 40 The numeral for VIII is 8

Step 2: Combine all the numbers according to the rules. Here we add them all together: CD (400) + XL (40) + VIII (8) = 448. Therefore, the numeral of CDXLVIII is 448.

We follow a pattern when it comes to writing Roman numerals. In this section, we will write some numbers related to the Roman numeral CDXLVIII: 

• Subtraction Rule: Only certain symbols can be subtracted, such as I from V and X, and X from L and C.
   
• Addition Rule: When a smaller numeral follows a larger numeral, add the smaller numeral to the larger one.
   
• Place Value: In Roman numerals, the sequence of symbols determines their value; numerals like I, X, C, and M can be combined with others to adjust value.
   
• Repetition Rule: Symbols like I, X, C, and M can be repeated up to three times in succession.
   
• Grouping Method: A technique used to simplify writing Roman numerals by breaking them down into logical groups, facilitating easier calculations.