Roman Numeral Conversion Exercises

How To Enter Data

• Single click on the pictured Roman Numerals at the upper part of the display (above the red display area).  The selected Roman Numeral will then be displayed in the red display area, if it passes syntax check.  If it passes and the Running Total checkbox is checked, then a total will appear in the message area or an okay if the Running Total checkbox is not checked.  If it fails syntax or rules verification, then the reason will be displayed in the message area.

• The top of the display has an edit box.  Initially it says hello.   This is where you will enter integer values for displaying in Roman Numeral with the ShowMe button in Just Practicing exercises or in entering integer values in the Roman To Decimal exercises.

• The red lightning mark after the M in the Roman Numeral selection area is the erase entry.  Click on the lightning mark and the last Roman Numeral you successfully entered will be erased.

The Conversion Exercises Can Follow 3 Methods Of Interpretation:

• Just Practicing -- Click on Roman Numeral Characters to add them to your number.   If you have the Running Total checkbox checked (default), then you will see the total displayed in the message area at the bottom of the display, along with various error messages.  Also if you enter a decimal number in the text entry area at the top of the display and press the ShowMe button, then the Roman Numeral equivalant will be displayed in the red display area.  You can select any of the three below described methods of Roman Numeral behavior to see how the historical progression may have occurred.
• Decimal To Roman -- A number will be displayed in the edit box at the top of the display.  You will then click on the Roman Numeral characters to add them to your number.  Then press the Answer button when finished.  To make it more challenging, uncheck the Running Total checkbox and the totals will not be displayed in the message area as you choose Roman Numeral characters.
• Roman To Decimal -- A Roman Numeral number will be displayed in the Red display area.   You will then enter a decimal number in the text entry area at the top of the display.  Then press Answer to test your choice.  To see the answer, press the ShowMe button and the correct decimal number will be displayed in the entry area.

Each Of The Above Methods Can Use The Following 3 Types Of Roman Numeral Behavior.

• Historical Beginnings -- Shown for information purposes only what the early application of Roman Numerals would be like.  There were no groupings of numbers from higher to lower, just entry of Roman letters that directly represent a number.  So you can enter a V, then an X, then an I.  In this method, every time you see an X, you add ten, each time you see an I, you add 1, etc.  Each number would be successively added to obtain the result.  You can see how confusing this would become as the numbers become larger.
• Historical Ordering -- Shown for information purposes only how or why a more orderly form of entering the Roman Numerals would evolve from the Historical Beginnings example.   Numbers are ordered from higher value on the left to lower values to the right.   Each of the same valued numbers are also grouped together, ie. all the I's are together and all the X's are together.  You can see how much easier it is to understand than having no order as in the Historical Beginnings example.
• Current Usage -- This is how we understand the current usage of Roman Numeral entry to be.  For compression purposes a method of subtraction was introduced by the users of Roman Numerals to the rules for writing and interpreting the Roman Numeral values.   The rules as we understand them are shown below.

Brief Note About Place Value

Although there is no column indication of place value that the decimal numbering system has where each column of numbers represents a place value such as 1's, 10's, etc. the current usage of Roman Numerals does group similar place values together.   The place values used can be understood to be based on base 10 with characters for groups of 5's introduced as well. The numbers progress as a base 10 system with groups of 5 characters for compression.  Using groups of 5 also incorporates the natural grouping of 5 a hand being 5 fingers.  So in addition to the base ten characters, inbetween each base value character there is a group of 5 of lower of the two values character.  So inbetween I and X ( 1 and 10 ) there is a V (5).  Inbetween X and C ( 10 and 100 ) there is a L (50). You can see how it is shorter to write VII for seven rather than IIIIIII and also a bit more intuitive from a human perspective as 1 hand plus 2 fingers from the other hand.

Characters With Overscores

When there is an overscore above the number, this is a representation of 1000 times that number, so a V with an overscore is representative of 5000, and X with an overscore is representative of 10000.  You can choose to have these characters used by checking or unchecking the Overscore checkbox, default is unchecked..  During the play of the exercises, the possible numbers will be increased or decreased to account for the overscore characters.  So numbers will be lower with the overscore checkbox unchecked.

Rules For Writing And Interpreting Roman Numeral's

The higher values are shown to the left and descend in value as you go to the right.   The Roman's introduced a method of subtraction that compresses the length of the number, as in displaying 9, IX can be used which subtracts I (1) from X (10) to result in 9.  Without the subtraction method VIIII would be used or IIIIIIIII. In interperating the rules for valid subtraction ordering you need to look at a subtraction combination such as XC (10 from 100) to be of a place value of 10's.  Then before the XC, higher place values should be entered and after the XC, lower place values.  So you could not enter LXC which would be 50 + (100-10).  The 50 is a group of 10's and the 10 from 100 is a group of 10's.   You could enter CXC which would be 100 + (100-10) or 190, as the 100 is a group of 100's and the 10 from 100 is a group of tens.  Also after the XC, you could enter V or I's, as they are less than the 10's place values. 

• Similar place values are displayed together.  This keeps in mind that two different characters can be used to represent one place value.  Such as IX to represent the place value of 1's (9, 1's)

• Place values of base 10, I (1), X (10), C (100), etc, can have up to 4 in a row using the current usage option.  Then the next character with higher value should be used.  ie. to display 6, use VI instead of IIIIII..  Many usages use the subtraction method, which for 1 less than the next group of 5, eg. 4, a subtraction will be used to subtract 1 from 5 to mean 4. ie. instead of IIII, IV can be written or for 9, IX can be used rather than VIIII.  We have allowed either of these to work when you enter them in the Decimal to Roman exercises, but for all of our representations, we will use the subtraction method for the afore mentioned case.  All groups of 5 can only have 1 in a row, as you could just use the group of ten to display it.  ie. for 10, an X is used rather than VV.

• Higher place values displayed on left and descend as you go to the right.

• Entering a higher character after a lower character means you are subtracting the lower character from the higher character.  ie. IX means to subtract 1 from 10.

• You can only use 2 successive characters for subtracting. ie. IXC is not valid as it is trying to represent a successive subtraction, as well as going up in place value.

• You can only subtract with the base ten characters.  ie. VX is not 5 from 10. or VC is not 5 from 100.

• A subtraction pair is understood to be the place value of the base ten value of the character used to subtract.  ie. XC is taken to be of the place value of 10's.  So any successive numbers should be of lower place value, such as V (5) or I (1).  Any characters to the left of the XC should be of higher base ten place values, such as C (100), D (500), etc.

Example In Table Form Of The Place Value Progession And Ordering

Quick Reference

Some History of Numbers and Number Base Systems

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Last update on 12/05/01

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