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Roman Numerals
Questions and answers related to the symbols used by the ancient Romans to represent numbers. These include the numerals: I, V, X, L, C, D and M.
14,167 Questions
What are two ways of adding together 19 49 and 99 using Roman numerals throughout both calculations?
19 = XIX
49 = XLIX
99 = XCIX
Expected result is 167 = CLXVII
Method 1: Convert subtractive pairs so IV becomes IIII, XL becomes XXXX and XC becomes LXXXX. Then sort values in descending order of value, grouping C, X and I in groups of 5, and L and V in groups of 2, then reduce these groups so that IIIII becomes V, VV becomes X, XXXXX becomes L and LL becomes C.
XIX + XLIX + XCIX =
XVIIII + XXXXVIIII + LXXXXVIIII =
L + XXXXX + XXXX + VV + V + IIIII + IIIII + II =
L + XXXXX + XXXX + VV + VV + V + II =
L + XXXXX + XXXXX + X + V + II =
LL + L + X + V + II =
C + L + X + V + II =
CLXVII
Method 2: Expand all symbols into positive and negative symbols, sort by absolute value, cancel out any similar values with opposing signs. Convert higher values to lower values as required.
XIX + XLIX + XCIX =
X - I + X - X + L - I + X - X + C - I + X =
C + L + X + X - X + X - X + X - I - I - I =
C + L + X + X - I - I - I =
C + L + X + V + V - I - I - I =
C + L + X + V + I + I + I + I + I - I - I - I =
C + L + X + V + I + I =
CLXVII
Under todays rules governing the Roman numeral system, which had nothing to do with the Romans themselves because they were introduced after the Dark Ages, 1999 is now officially considered to be MCMXCIX which is rather remarkable inasmuch that mathematical integration with other numerals is hardly possible.
But there is evidence to suggest that the Romans would have actually calculated the equivalent of 1999 on an abacus counting device as MDCCCCLXXXXVIIII and then probably abridged it to IMM (2000-1) in written format thus facilitating the speed and ease of addition as follows:-
IMM+DCLXVI = MMDCLXV (2000-1)+(666) = (2665)
Alternatively:-
MDCCCCLXXXXVIIII+DCLXVI = MMDCLXV (1999)+(666) = (2665)
Note that: 5*I=V, 2*V=X, 5*X=L, 2*L=C, 5*C=D and 2*D=M
Roman numerals: M=1000, D=500, C=100, L=50, X=10, V=5 and I=1
QED
Nowadays we would convert the equivalent of 99, 1776 and 1900 into Roman numerals as XCIX, MDCCLXXVI and MCM respectively which inhibits their ability to interact with each other:-
But the ancient Romans probably added the equivalent of 99, 1776 and 1900 in either of the following formats:-
IC+MDCCLXXVI = MDCCCLXXV => (100-1)+1776 = 1875
MDCCCLXXV+CMM = MMMDCCLXXV => 1875+(2000-100) = 3775
Alternatively:-
LXXXXVIIII+MDCCLXXVI = MDCCCLXXV => 99+1776 = 1875
MDCCCLXXV+MDCCCC = MMMDCCLXXV => 1875+1900 = 3775
Values: M=1000, D=500, C+100, L=50, X=10, V=5 and I=1
Note: 5*I=V, 2*V=X, 5*X=L, 2*L=C, 5*C=D and 2*D=M
QED
What are a score and five more interesting facts about the ancient Roman numeral system?
1 Its symbol for nought is N which is not needed
2 Its numerals have positional place values that are self evident
3 It once needed only 5 symbols which were I V X L and C
4 It used single or multiple brackets to increase the values of numerals
5 It once was I) for 500 and (I) for 1000 later changed to D and M
6 Its values are: M=1000 D=500 C=100 L=50 X=10 V=5 and I=1
7 It needs less numerals than todays Hindu-Arabic numeral system
8 It used superscripted numerals to increase the value of numerals
9 Its equivalent of 1,000,000,000,000 is (M)(M) or 1.0*1012 in scientific notation
10 It doesn't use decimals
11 It used fractions only to a limited extent
12 It's still used extensively today
13 It;s used by VIPs to nominate their names
14 It never used IV for 4 for fear of offending the Roman god Jupiter
15 It's quite capable of performing the 4 operations of arithmetic
16 Its numberals can sometimes be abridged yet retaining their original values
17 It was conceived by the Etruscans who once ruled the Romans
18 Its original rules governing it were changed in the Middle Ages
19 It's now MMXIV for 2014 but it once was MMXIIII or as IMMXV
20 It's the perfect prerequisite to learning algebra
21 It was superseded by the Hindu-Arabic numeral system in the Middle Ages
22 It once was calculated on a beaded abacus counting device
23 Its fractional equivalent of a 1/2 is S
24 Its equivalent of VIIIS is SIX which means 8.5 = 10-1.5
25 It was Julius Caesar who used Roman numerals in his calculations to extend the Roman year of 10 months to 12 months known as the Julian calendar which was modified in the year of MDLXXXII (1582) by Pope Gregory XIII (13) known today as the Gregorian calendar
What is the numeric value of 245.18?
It is exactly what is implied in the question 245.18 but expressed as an improper fraction it is 12259/50
Notwithstanding the fact that in todays modern notation of Roman numerals 999 is now considered to be CMXCIX inasmuch that the ancient Romans would have probably subtracted the given numbers in either of the following formats:-
As: MDCCLXXVI-IM = DCCLXXVII => 1776-(1000-1) = 777.
Or as: MDCCLXXVI-DCCCCLXXXXVIIII = DCCLXXVII => 1776-999 = 777.
For more complicated calculations the Romans would have used an abacus calculating device.
QED
How many numbers were there originally in Arabic numerals?
10
there arrangement was used to develop Arabic numbers like adding two numbers of the 10 together to get a big number (ex.: 12) and arranging three numbers of the 10 together to get a bigger number (ex.: 256) and so on just like English numbers
In what products do gas tubes find application?
Product types included diodes, rectifiers, control-type industrial triodes, hydrogen and nonhydrogenthyratons, and other gas and vapor tubes.
What risks are associated with D and X?
associated emotional reactions.heavy bleeding.blood clots.damage to the cervix or uterus.pelvic infection.incomplete abortion.Possible long-term risks include difficulty becoming pregnant or carrying a future pregnancy to term.
There is no doubt that the ancient Romans would have calculated the equivalent of 1999 on an abacus counting device as MDCCCCLXXXXVIIII and as evidence suggest abridged it to IMM (2000-1) in written form.
Yet in accordance with the rules governing todays Roman numeral system drawn up in the Middle Ages, presumably to make Roman numerals more compatible with Hindu-Arabic numerals that were being introduced into Western Europe at the time, nowadays we would convert 1999 into Roman numerals as MCMXCIX which is unfinished business as far as addition goes because those numerals actually represent M+CM+XC+IX and when added together they too abridge to IMM as in the following manner:-
M+CM = CMM => 1000+(1000-100) = (2000-100) = 1900
CMM+XC = XMM => (2000-100)+(100+10) = (2000-10) = 1990
XMM+IX = IMM => (2000-10)+(10-1) = (2000-1) = 1999
If we were to add M+CM+XC+IX as CM+IX+M+XC they too would still total to IMM.
So it follows that 1999 in Roman numerals is MDCCCCLXXXXVIIII which can be abridged to IMM in the same way that LXXXVIIIIS (89.5) can be abridged to SXC (100-10.5) in which author David Eugene Smith noted in his book 'History of Mathematics' volume 2 first published in 1925 and ISBN 0486 204 308
Note: M=1000, D=500, C=100, L=50, X=10, V=5, I=1 and S=1/2 or 0.5
QED by David Gambell
The rules as we know them today now governing the Roman numeral system had absolutely nothing to do with the ancient Romans whatsoever because they were introduced during the Middle Ages and so the given numbers when converted into Roman numerals are now considered to be MCMXCIX, CXCIX and XIX respectively but the Romans themselves would have most probably calculated them in either of the following formats:-
IMM+ICC+IXX = MMCCXVII => (2000-1)+(200-1)+(20-1) = 2217
MDCCCCLXXXXVIIII+CLXXXXVIIII+XVIIII = MMCCXVII => 1999+199+19 = 2217
The above calculations were quite simple and straightforward to work out but for more complicated calculations the Romans would have used an abacus calculating device.
QED
What does 7u equals -6v-44 plus 3u equals 14v plus 64 equal?
7u = -6v - 44 + 3u = 14v + 64
The first two give: 4u = -6v - 44
and the first and third give: 7u = 14v + 64
Then 7*the first of these minus 4 times the second give:
28u - 28u = -42v -308 - 56v - 256 = -98v -564
So 98v = -564 and so v = -282/49 =
And then 7u = 14*(-282/49) + 64 = -116/7
so that u = -116/49
Solution:
u = -116/49 = -2.3673 to 4 dp
v = -282/49 = -5.7551 to 4 dp
Another Answer:-
If the question was meant to be: 7u = -6v-44 and 3u = 14v+64
Then by a process of multplication and elimination the solution to this simultaneous equation would work out as: u = -2 and v = -5
The way in which we write out Roman numerals today differs in many respects as to the way that the Romans actually did themselves to the extent that today we would convert 19, 49, 99 and 1999 into Roman numerals as XIX, XLIX, XCIX and MCMXCIX respectively thus making addition of them almost impossible.
But notwithstanding the aforementioned inasmuch that there is evidence to suggest that the Romans in the past would have calculated the above numbers as in either of the following formats:-
IXX+IL = LXVIII (20-1)+(50-1) = (68)
LXVIII+IC = CLXVII (68)+(100-1) = (167)
CLXVII+IMM = MMCLXVI (167)+(2000-1) = (2166)
Alternatively:-
XVIII+XXXXVIIII = LXVIII (19)+(49) = (68)
LXVIII+LXXXXVIIII = CLXVII (68)+(99) = (167)
CLXVII+MDCCCCLXXXXVIIII = MMCLXVI (167)+(1999) = (2166)
Note that: 5*I=V, 2*V=X, 5*X=L, 2*L=C, 5*C=D and 2*D=M
Roman numerals: M=1000, D=500, C=100, L=50, X=10, V=5 and I=1
QED
