Question

Write the following Roman numerals in ascending order:
CXIX, XCIX, CXXI, CIX, CXX

Answer 1

Hint: First write all the given Roman numerical. Now assume a variable to each of the roman numerical. Now convert the roman numerical into Arabic numbers as arranging the Arabic numbers is very easy compared to the Roman numerical.

Complete step-by-step answer:
Roman numerals: - Roman numeral system is a numeral system where numerals are defined by combination of the letters I, V, X, L, C, D and M which are used in various orders to stand for a specific number \[X = 10,{\rm{ C = 100, V = 5, I = 1}}\]
Given roman numerals in the question can be written as:
CXIX, XCIX, CXXI, CIX, CXX
Let us assume the value of variable a be the roman CXIX.
Let us assume the value of variable b be the roman XCIX.
Let us assume the value of variable c be the roman CXXI.
Let us assume the value of variable d be the roman CIX.
Let us assume the value of variable e be the roman CCX.
The romans are divided into parts such as, first see the first letter. Next, look at the next letter if it is greater then we must subtract the first from the letter or else you must add.
Case I: - Solving the value of “a”, can be written as:
\[a = CXIX\]
We write a as sum of numerals, \[a = C + X + IX\]
By substituting their values, we get value of a as, \[a = 100 + 10 + 9\]
By above equation, we can say the value of a to be as:
\[a = 119{\rm{ }}\] ……………..(1)
Case II: - Solving the value of b can be written as: \[b = XCIX\]
By writing b as the sum of numerals, we get it as: \[b = XC + IX\]
By substituting the values of those, we get b as: \[b = 90 + 9\]
By above equation, we get value of b as:
\[ = 99\] ……………..(2)
Case III: - We have variable c as, \[c = CXXI\]
By writing c as the sum of numerals, we get it as: \[c = C + X + X + I\]
By substituting their values, we get c as: \[c = 100 + 10 + 10 + 1\]
By above equation, we get value of c as:
\[c = 121\] ……………..(3)
Case IV: - We have variable d as, \[d = CIX\]
By writing d as the sum of numerals, we get it as: \[d = C + IX\]
By substituting their values, we get d as: \[d = 100 + 9\]
By above equation, we get value of d as:
\[d = 109\] ……………..(4)
Case V: - We have variable d as, \[e = CXX\]
By writing d as the sum of numerals, we get it as: \[e = C + X + X\]
By substituting their values, we get d as: \[e = 100 + 10 + 10\]
By above equation, we get value of d as:
\[e = 120\] ……………..(5)
By equation (1), (2), (3), (4), (5); we can say order of a, b, c, d, e as:
\[{\rm{b}} < {\rm{d}} < {\rm{a}} < {\rm{e}} < {\rm{c}}\]
By substituting the romans into above inequality, we get it as:
\[{\rm{XCIX}} < {\rm{CIX}} < {\rm{CXIX}} < {\rm{CXX}} < {\rm{CXXI}}\].
Therefore, this is the required order asked in the question.

Note: Be careful while converting romans to Arabic, even if you add instead of difference while converting it into Arabic you will get a large difference in answer as all the numbers are so close. Do the conversion properly, as it is the only basic step to reach the result. Generally students confuse between XC, CX, Remember \[{\rm{XC}} = {\rm{9}}0,{\rm{ CX}} = {\rm{11}}0\], it is very important.