MATH SOLVE

4 months ago

Q:
# What is 346 in Roman Numerals?

Accepted Solution

A:

Solution: 346 in Roman Numerals is CCCXLVI
Methods
How do Roman Numerals Work?
Used commonly until about the 14th Century, Roman Numerals served as a tool for everyone in Western cultures. Eventually this system was replaced by the Hindu-Arabic number system, which was more advantageous for mathematics and other more complex uses. The more modern version of the Roman Numerals system is based on several Roman letters that associate with a particular integer/number (some of these Roman letters are X, V, D). Put it simply, here is a list of the 7 different letters and what numerical value they hold:
To get a head start on how these work, take a look at this next table - it has many common numbers that are used to convert regular numbers to Roman Numerals or vice-versa. With some help from the table above, can you identify any patterns? What rules do you think they’re using?
If you’ve gone through these tables, you might have realized what some of the rules are. If not, you will find the rules that one needs to abide by in order to write any number as a Roman Numeral successfully:
If you want a number that is a multiple of one of the 7 letters they use, its value is the sum of that value of that letter how many ever times it appears. For example: III = 3 because we repeated three I’s and I is 1.
Letters I, X, and C can be repeated a maximum of three times but not four or more. For example: XX = 20 because X = 10, so 10 + 10 = 20 = XX
Letters L, V, D, cannot be repeated at all - they must be unique for that number.
When you write a letter with a smaller value before a letter with a bigger value, you must subtract the smaller value from the bigger value. For example, IV is 4 because I = 1, V = 5, and since the letter I came before V, we must subtract: IV = 5 - 1 = 4.
When you write a letter with a smaller value after a letter with a bigger value, you must add the smaller value to the bigger value. For example, LX is 60 because L = 50, X = 10, and since X is after L, we must add: LX = 50 + 10 = 60
The letter I can be subtracted from V and X only and the letter X can only be subtracted from L, M and C.
Step-by-step: Converting 346 in Roman Numerals
Using the above rules and the basic 7 letters of the modern Roman Numerals, we can break down 346 into the following:
346 = 100 + 100 + 100 + 10 + 50 + 5 + 1 = CCCXLVI
As you can see, we can break down 346 by seeing which of the biggest numbers fit and then finding smaller ones to add up to/subtract while following the given rules. As a result, we see that 346 in Roman Numerals is CCCXLVI.
Roman Numerals Continued
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