Find the unit digit of the following numeric expressions.(i) 11420 +

1.	Find the unit digit of the following numeric expressions.(i) 11420 + 11521 + 11622(ii) 1000010000 + 1111111111
Answer» (i) 114²⁰ + 115²¹ + 116²² In 114²⁰ unit digit of base 114 is 4 and power is 20 (even power). ∴ Unit digit of 114²⁰ is 6. In 115²¹ unit digit of base 115 is 5 and power is 21 (Positive Integer). ∴ Unit digit of 115²¹ is 5. In 116²² unit digit of base 116 is 6 and power is 22 (Positive Integer). ∴ Unit digit of 116²² is 6. ∴ Unit digit of 114²⁰ + 115²¹ + 116²² can be obtained by adding 6 + 5 + 6 = 17. Unit digit of 114²⁰ + 115²¹ + 116²² is 7. (ii) 10000¹⁰⁰⁰⁰ + 11111¹¹¹¹¹ In 10000¹⁰⁰⁰⁰ the unit digit of base 10000 is 0 and power is 10000. Unit digit of 10000¹⁰⁰⁰⁰ is 0. In 11111¹¹¹¹¹ the unit digit of base 11111 is 1 and power is 11111. Unit digit of 11111¹¹¹¹¹ is 1. Unit digit of 10000¹⁰⁰⁰⁰⁰ + 11111¹¹¹¹¹ is 0 + 1 = 1

Find the unit digit of the following numeric expressions.(i) 11420 + 11521 + 11622(ii) 1000010000 + 1111111111

Answer»

(i) 114²⁰ + 115²¹ + 116²²

In 114²⁰ unit digit of base 114 is 4 and power is 20 (even power).

∴ Unit digit of 114²⁰ is 6.

In 115²¹ unit digit of base 115 is 5 and power is 21 (Positive Integer).

∴ Unit digit of 115²¹ is 5.

In 116²² unit digit of base 116 is 6 and power is 22 (Positive Integer).

∴ Unit digit of 116²² is 6.

∴ Unit digit of 114²⁰ + 115²¹ + 116²² can be obtained by adding 6 + 5 + 6 = 17.

Unit digit of 114²⁰ + 115²¹ + 116²² is 7.

(ii) 10000¹⁰⁰⁰⁰ + 11111¹¹¹¹¹

In 10000¹⁰⁰⁰⁰ the unit digit of base 10000 is 0 and power is 10000.

Unit digit of 10000¹⁰⁰⁰⁰ is 0.

In 11111¹¹¹¹¹ the unit digit of base 11111 is 1 and power is 11111.

Unit digit of 11111¹¹¹¹¹ is 1.

Unit digit of 10000¹⁰⁰⁰⁰⁰ + 11111¹¹¹¹¹ is 0 + 1 = 1