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# The difference between the smallest three digit number and the greatest two digit number is (a) I (b) XX (c) XC (d) C

Last updated date: 13th Aug 2024
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Hint:
Here, we need to find the difference between the smallest three digit number and the greatest two digit number. We will write the smallest three digit number and the greatest two digit number and subtract them to find the difference. Then, we will write the difference in roman numerals and hence, determine the correct option.

Complete step by step solution:
We will write the smallest three digit number and the greatest two digit number and subtract them to find the difference.
The smallest three digit number is 100.
The greatest two digit number is 99.
We will subtract 99 from 100.
Thus, subtracting the number 99 from the number 100, we get
$100 - 99 = 1$
Now, we need to write the difference 1 in roman numerals.
In roman numerals, I represents 1, V represents 5, X represents 10, L represents 50, C represents 100, D represents 500, and finally, M represents 1000.
The number 1 is represented by the roman numeral I.
Therefore, the difference between the smallest three digit number and the greatest two digit number is I.

Thus, the correct option is option (a).

Note:
Additional Information: We can check the numbers represented by the other options also.
In roman numerals, when a symbol comes after a larger symbol, the values are added.
For example: In LV, V comes after the larger symbol L. Thus, LV $= 50 + 5 = 55$.
When a symbol comes before a larger symbol, the values are subtracted.
For example: In XL, X comes before the larger symbol L. Thus, XL $= 50 - 10 = 40$.
In option (b), the number XX represents $10 + 10 = 20$.
In option (c), the symbol X comes before the larger symbol C. Thus, the number XC represents $100 - 10 = 90$.
In option (d), the number C represents 100.