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BasicsHow do I read and write Roman numerals?
A numeral is a symbol used to represent a number. (Our digits 0-9 are often called Arabic numerals.) Each letter used in Roman numerals stands for a different number:
A string of letters means that their values should be added together. For example, XXX = 10 + 10 + 10 = 30, and LXI = 50 + 10 + 1 = 61. If a smaller value is placed before a larger one, we subtract instead of adding. For instance, IV = 5 - 1 = 4. You can use these rules to write a number in Roman numerals. Convert one digit at a time. Let's try 982: From the Dr. Math archives:What are the rules for subtracting letters? Can I write MIM for 1999? What about IIII for 4?
Here are the official rules for subtracting letters: These rules only became official in the Middle Ages. Even today, not everybody follows them: you might notice that some clocks say IIII instead of IV. From the Dr. Math archives:How do I write large numbers? The biggest Roman numeral is M, for 1000, so one easy way to write large numbers is to line up the Ms: MMMMMMM would be 7000, for instance. This system gets cumbersome quickly. When they needed to work with many large numbers, the Romans often wrote a bar above a numeral. The bar meant to multiply by 1000. Using this method, 7000 would be . From the Dr. Math archives:Web Resources:
Calculators and Converters
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CalculationsDid the Romans use fractions? The Romans didn't have a standard way to write fractions using their numerals. Instead, they just wrote out the word for the fraction: for example, two-sevenths was "duae septimae" and three-eighths was "tres octavae." The Romans did not have a word for every imaginable fraction: how often do you need to say thirty-three seventieths? If necessary, they would probably have said something like, "thirty-three seventieth parts," or "triginta tres septuagensimae partes." The Romans did most of their practical calculations with fractions by using the uncia. The uncia started out as 1/12 of the as, a unit of weight (the word uncia is related to our word "ounce"), but it soon came to mean 1/12 of anything. You can add up twelfths to make halves, thirds, or quarters, so the uncia was fairly versatile. When they wanted smaller fractions, the Romans usually cut the uncia into smaller parts. The system is very similar to measuring length in inches and fractions of the inch: you might not measure an object's length exactly, but you can still come very close. There were Roman and medieval symbols for multiples of the uncia. The semis, which was six unciae, or one-half, was often represented by this symbol: . However, uncia symbols were never standardized, and not everybody used them. Some late medieval writers even substituted the modern fraction bar. From the Dr. Math archives:From the Web:How can I use Roman numerals to do arithmetic problems?
Let's start with an addition problem: 23 + 58. In Roman numerals, that's XXIII + LVIII. We'll begin by writing the two numbers next to each other: Now let's try another addition problem: 14 + 17, or XIV + XVII. Notice that the I in XIV is being subtracted, so this problem is going to be a little more complicated. We begin the way we did before, by writing the numbers side by side: There are similar methods for subtracting, multiplying, and even dividing Roman numerals. However, they can be frustrating, and for a good reason. Even the Romans didn't use them. When they wanted to do complicated arithmetic problems, the Romans used a special counting board or an abacus. A Roman counting board looked something like this: Counters, such as pebbles, were placed in each column. The columns were often grooved, so that the pebbles wouldn't roll away. A pebble in the bottom half of the board meant one, ten, one hundred, or one thousand, depending on its placement. A pebble in the top half had its value multiplied by five.
There were many variations on the Roman counting board, such as extra columns for larger numbers. People in the Middle Ages turned the columns the other way and drew lines down the middle, so that the board could hold several numbers at once. This board was designed for flat counters. Counters were placed on the line for I, X, C, and M, and between lines for V, L, and D. The little x on the M line is like the modern comma in 1,000: it helps you remember the meaning of each numeral's position.
Here's an example of multiplication.
Try making your own board and doing calculations with stones or pennies. By practicing on a counting-board or abacus, you can become quite fast. However, some multiplication and most division problems are still very complicated. People who needed to do many multiplications or divisions probably looked the answers up in a table, or hired someone who could. From the Dr. Math archives:From the Web:[Top]
Uses Past and PresentHow did the Romans use math?
Unlike the ancient Greeks, the Romans weren't particularly interested in "pure" math, such as theorems about abstract geometry. They used their mathematics for more practical purposes, such as building roads, bridges, and temples out of stone, keeping accounts, and supplying their armies. People went on using Roman numerals for hundreds of years after the Roman empire fell. You might have needed Roman numerals in the Middle Ages to build a fortress, calculate the date of Easter, or sell a shipment of wool. From the Dr. Math archives:From the Web:How are Roman numerals used today?
People use Roman numerals From the Dr. Math archives:From the Web:Resources for other numeral systems
From the Dr. Math archives:General: From the Web:General: |
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