400 in Roman numerals

When we write 400 in Roman numerals, it is represented by CD. Roman numerals are a unique system of numbers that existed in ancient Rome, in which letters of the Latin alphabet were assigned numerical values. By combining these letters, various numbers can be formed. 

In this lesson, we’ll explore how to write 400 in Roman numerals, learn the simple rules behind it, and go through step-by-step examples to make it super easy to understand.

 

Table of Contents

• How to Write 400 in Roman Numerals?
• Basic Rules to Write Roman Numerals
• Roman Numerals Related to the Number 400
• 400 in Roman Numerals - Solved Examples
• Conclusion
• FAQs on 400 in Roman Numerals

 

How to Write 400 in Roman Numerals?

Roman numerals are expressed using distinctive letters, each representing a set number. Two important symbols you should remember here are:

• C = 100

• D = 500

Now consider the number 400. When we compare it to the closest larger Roman numeral, 500, we realize that 400 is precisely 100 less than 500.

Here comes the important rule of Roman numerals:

When a smaller digit is placed in front of a larger digit, subtraction is indicated.
So, to represent 400, we take 500 (D) and subtract  100 (C) from it. That is represented as: 

500 - 100 = 400

D - C = CD

Thus, the Roman numeral for 400 is CD. 

 

Basic Rules of Roman Numerals

• A symbol is added to itself if repeated.
  Example: II = 2, XX = 20

• A symbol can be repeated only 3 times.
  Example: XXX = 30

• Symbols V (5), L (50), and D (500) are never repeated.

• If a smaller symbol comes after a larger one, we add.
  Example: VI = 5 + 1 = 6

• If a smaller symbol comes before a larger one, we subtract.
  Example: IV = 5 - 1 = 4

• I can only be subtracted from V and X.
  X can only be subtracted from L, C, and M.
  C can only be subtracted from D and M.
  
  

 

Roman Numerals Related to the Number 400

Understanding how to write 400 in Roman numerals helps us easily form numbers around it using simple addition and subtraction rules. Roman numerals follow a pattern where smaller numbers placed before larger numbers are subtracted, and smaller numbers placed after larger numbers are added.

The number 400 in Roman numerals is written as CD. This comes from the fact that 500 (D) minus 100 (C) equals 400, hence CD.

Once we know this, we can write numbers close to 400 step by step:

• 401 = CDI
  To get 401, we simply add 1 to 400. Since 1 is written as I, 400 + 1 = CD + I = CDI.

• 402 = CDII
  Adding 2 gives CD + II = CDII.

• 403 = CDIII
  Adding 3 gives CD + III = CDIII.

• 404 = CDIV
  Adding 4 is slightly different because 4 is written as IV (5 - 1). So, 400 + 4 = CD + IV = CDIV.

• 405 = CDV
  Adding 5 gives CD + V = CDV.

• 406 = CDVI
  Adding 6 gives CD + VI = CDVI.

• 407 = CDVII
  Adding 7 gives CD + VII = CDVII.

• 408 = CDVIII
  Adding 8 gives CD + VIII = CDVIII.

• 409 = CDIX
  For 9, we use IX (10 - 1). So, 400 + 9 = CD + IX = CDIX.

• 410 = CDX
  Adding 10 gives CD + X = CDX.

• 450 = CDL
  To write 450, we add 50 (L) to 400. So, 400 + 50 = CD + L = CDL.

• 490 = CDXC
  Adding 90 is written as XC (100 - 10). Therefore, 400 + 90 = CD + XC = CDXC.

• 499 = CDXCIX
  This number combines several rules: 400 (CD) + 90 (XC) + 9 (IX) = CDXCIX.

By understanding 400 as CD, you can easily build numbers around it by adding or subtracting smaller Roman numerals.

 

400 in Roman Numerals - Solved Examples

Example 1: Write the Roman numeral for 400.

Solution:

We know that D = 500 and C = 100.

To find 400, we notice that it is 100 less than 500.

In Roman numerals, when a smaller number comes before a larger number, we subtract it.

So, 500 - 100 = 400, which is written as CD.

Therefore, 400 in Roman numerals is CD.

 

Example 2: What should be subtracted from D to get CD?

Solution:

We know that D = 500 and CD = 400.

We need to find the number that, when subtracted from 500, gives 400.

500 -? = 400

? = 100

In Roman numerals, 100 is C.

So, D - C = CD.

 

Example 3: Write the product of 400 × 2 in Roman numerals.

Solution:

First, calculate the product: 400 × 2 = 800.

Now, we convert 800 into Roman numerals.

500 + 100 + 100 + 100 = 800

In Roman numerals: D + C + C + C = DCCC

So, 400 × 2 = DCCC.

 

Example 4: Find the difference between CM (900) and CD (400).

Solution:

We are given: CM = 900 and CD = 400.

To find the difference: 900 - 400 = 500.

In Roman numerals, 500 = D.

So, CM - CD = D.

 

Example 5: Express the sum of CD (400) + XC (90) in Roman numerals.

Solution:

We are given CD = 400 and XC = 90.

To find the sum: 400 + 90 = 490.

Now, convert 490 into Roman numerals:

400 + 90 = CD + XC = CDXC

So, CD + XC = CDXC.

 

Conclusion

The Roman numeral for 400 is CD, which follows the subtraction rule (500 - 100). Understanding this makes it easy to learn other numerals like 900 (CM) and 90 (XC). Roman numerals are still seen on clocks, monuments, and even in movie titles, keeping history alive in our daily lives.

 

Frequently Asked Questions on 400 in Roman Numerals

1. What is 400 in Roman numerals?

Answer: 400 in Roman numerals is CD.

 

2. Why is 400 written as CD and not CCCC?

Answer: Roman numeral rules do not allow a symbol to be repeated more than 3 times. Instead, we use subtraction: 500 - 100 = 400 → CD.

 

3. How is 500 written in Roman numerals?

Answer: 500 in Roman numerals is D.

 

4. What comes after 400 in Roman numerals?

Answer: After 400 (CD), we have 401 = CDI, 402 = CDII, and so on.

 

5. How do we write 900 in Roman numerals?

Answer: 900 in Roman numerals is CM (1000 - 100).

 

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