Find the unit digit of 4198 + 612345 + 34866 + 2411 + 1.

Concept

The unit digit of a sum of several numbers depends only on the unit digits of the numbers being added — carries generated while summing only affect digits to the left (tens, hundreds, ...), never the units place of the final total. So the unit digit of the sum equals the unit digit of the sum of the individual unit digits.

Application

1. Identify the unit digit of each number:

   • The number 4198 has a unit digit of 8.

   • The number 612345 has a unit digit of 5.

   • The number 34866 has a unit digit of 6.

   • The number 2411 has a unit digit of 1.

   • The number 1 has a unit digit of 1.

2. Add the unit digits together:

   • 8 + 5 + 6 + 1 + 1 = 21.

3. Find the unit digit of the sum:

   • The sum of the unit digits is 21.

   • The unit digit of 21 is 1.

Cross-check

Adding the numbers directly confirms this: 4198 + 612345 + 34866 + 2411 + 1 = 653821, whose unit digit is also 1.