Question

Bobby's date of birth is 19th September. Express the date in Roman system.
A. XXI
B. XIXX
C. IIX
D. XIX

Answer 1

Hint:
Roman Numerals:

Number	Roman Numeral
1	I
5	V
10	X
50	L
100	C
500	D
1000	M
...	...

A Smaller Roman Numeral written before another Roman Numeral is subtracted from its value and a Smaller Roman Numeral written after another Roman Numeral is added to its value.
Also, a maximum of three 'I' can be used together. Four 'I' are NOT used together.
e.g. $IIX=10-1-1=8$, $XV=10+5=15$ etc.

Complete step by step solution:
We know that "A Smaller Roman Numeral written before another Roman Numeral is subtracted from its value and a Smaller Roman Numeral written after another Roman Numeral is added to its value." And the only symbols available are 1, 5, 10, 50 and so on.
Observe that $9=10-1=IX$ .
We cannot write 9 as $5+4=VIIII$ because four 'I's are not written together.

∴ 19 can be written as $10+9=X\left( IX \right)=XIX$.

Note:
1) XIX is NOT read as (XI)X because the numeral occurring 'before or after a single numeral' must be smaller.
2) Numbers '1', '2' and '3' are represented as 'I', 'II' and 'III' but the number '4' is written as 'IV' and NOT AS 'IIII'.
3) Roman system is a counting system. There is no zero in the system, and negative integers and fractions are not represented in it, for which the decimal system was developed later.
4) The numbers in Roman system have symbols for 1, 5, 10, 50, 100, 500, ... etc. These are multiples of 5.
5) The Roman system is an improvement over the Tally system of counting.