Is the Roman numeral DCDCXCX valid or not? How to convert MC? Write it as a Hindu-Arabic number. Turn the number written with letters (symbols) in the Roman numeral system

Is the entered Roman numeral, DCDCXCX, valid or not?

1. The Roman numerals used to make the conversion:

X = 10; C = 100; D = 500;

The basic reading rules of the Roman numerals

The numerals and the groups of numerals written in subtractive notation must be written from left to right, in descending order, by their value, from high to low. Some symbols (letters) can be repeated up to 3 times in a row: I, X, C, M, (X), (C), (M).

A group of Roman numerals written in subtractive notation = a group of two numerals (two letters), one of a lower value preceding another larger one. The only allowed subtractive groups are these: IV, IX, XL, XC, CD, CM, M(V), M(X), (X)(L), (X)(C), (C)(D), (C)(M). To calculate the value of a group subtract the value of the first symbol from the value of the second.
The subtractive notation in the writing of the Roman numerals

A group of Roman numerals written in additive notation = a group of two or more numerals (letters), of equal value or sorted in descending order, by their value, from high to low. To calculate the value of the group, add up the values of the symbols that make up the group.
The additive notation in the writing of the Roman numerals


2. The groups of numerals written in subtractive notation:

DCDCXCX

CD = D - C = 500 - 100 = 400;

XC = C - X = 100 - 10 = 90;


DCDCXCX is not a valid Roman numeral.

3. Why is the Roman numeral not valid?

DCDCXCX: A group of numerals in subtractive notation, CD ( = 400), cannot be placed after a numeral, D ( = 500), of the same range value (100 - 900).

DCDCXCX: The numeral C ( = 100) cannot be placed after a group of numerals in subtractive notation, CD ( = 400), of the same range value (100 - 900).

DCDCXCX: The numeral X ( = 10) cannot be placed after a group of numerals in subtractive notation, XC ( = 90), of the same range value (10 - 90).


4. Please correct or remove (some of) the symbols numerals:

DCDCXCX


How to convert the Roman numeral:
MC
written as a Hindu-Arabic number
(the numbers we use every day)

1. The Roman numerals used to make the conversion:

C = 100; M = 1,000;

The basic reading rules of the Roman numerals

The Roman numerals must be written from left to right in descending order, by their value. Some symbols can be repeated up to 3 times in a row: I, X, C, M, (X), (C), (M).

A group of Roman numerals written in additive notation = a group of two or more numerals (letters), of equal value or sorted in descending order, by their value, from high to low. To calculate the value of the group, add up the values of the symbols that make up the group.
The additive notation in the writing of the Roman numerals


MC is a valid Roman numeral.

MC meets all the rules of writing Roman numerals.


2. Calculate the value of the Roman number.

Add up all the values of the individual Roman numerals:

MC =

M + C =

1,000 + 100 =

1,100


MC is a group of numerals written in additive notation.

Check the result (reverse the process).
How to convert the number 1,100

1. Break the number down to place value subgroups (decompose it):

1,100 =

1,000 + 100;


2. Convert each subgroup:

1,000 = M;

100 = C;


3. Wrap up the Roman numeral (construct it):

1,100 =

1,000 + 100 =

M + C =

MC;


The final answer:

DCDCXCX is not a valid Roman numeral.

MC = 1,100

MC
written as a Hindu-Arabic number
(the numbers we use every day)

More operations of this kind:

MXCIX = ?

MCI = ?

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The set of basic symbols of the Roman system of writing numerals

The major set of symbols on which the rest of the Roman numberals were built:

(*) These numbers were written with an overline (a bar above) or between two vertical lines. Instead, we prefer to write these larger numerals between brackets, ie: "(" and ")", because:

(*) An overline (a bar over the symbol), two vertical lines or two brackets around the symbol indicate "1,000 times". See below...

Logic of the numerals written between brackets, ie: (L) = 50,000; the rule is that the initial numeral, in our case, L, was multiplied by 1,000: L = 50 => (L) = 50 × 1,000 = 50,000. Simple.

(*) At the beginning Romans did not use numbers larger than 3,999; as a result they had no symbols in their system for these larger numbers, they were added on later and for them various different notations were used, not necessarily the ones we've just seen above.

Thus, initially, the largest number that could be written using Roman numerals was:

The reading rules of the Roman numerals, summary:

I. The set of the basic symbols of the Roman numerals

II. The rule of the repetition of the Roman numerals

III. The groups of the Roman numerals written in subtractive notation

IV. The additive notation of the Roman numerals

How to convert the Hindu-Arabic numbers to Roman numerals: breaking down the numbers into place value subgroups

Examples of converting Hindu-Arabic numbers to Roman numerals

Two lists of the first Roman numerals (in ascending order):

The list of the first 100 Roman numerals: the Roman numerals from 1 to 100

The list of the first 1,000 Roman numerals: the Roman numerals from 1 to 1,000

Mathematical operations with Roman numerals:

I. Addition. Learn by an example how to add the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

II. Subtraction. Learn by an example how to subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations

III. Addition and subtraction. Learn by an example how to add and subtract the Roman numerals the right way, like the Romans were calculating, without the use of the Hindu-Arabic numbers. Steps, explanations