This system of "units digit arithmetic" may seem like abstract nonsense -- when would you need to compute just with units digits? In fact, different algebraic systems arise in all kinds of applications. Note 9
In the past few activities, you have been looking at a modular system. The "mod 10" system means you divide by 10 and take the remainder -- in other words, take the units digit. We'll now focus on an application involving another modular system: enciphering and deciphering messages.
First, notice that you can assign each letter of our alphabet a number from 0-25:
One of the oldest known substitution ciphers (a code where one letter stands for another) is the one reportedly used by Julius Caesar himself:
To get the ciphered letter, add 3 to the original letter, or "plaintext." In symbols, this is: C = P + 3. Note 10