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WHAT IS THE TENS DIGIT IN 2003 TO THE POWER OF 2003

WHAT IS THE TENS DIGIT IN 2003 TO THE POWER OF 2003

Grade:10

1 Answers

Vikas TU
14149 Points
6 years ago
If the units digit of a number N is 3, then the units digit of N^2 will be 9, for N^3 it will be 7, for N^4 it will be 1 and then it will repeat (N^5 will be 3 again, N^6 will be 9 again and so on).  
For the last two digits, it will repeat after 20 iterations (so if N^1 ends with 03, then N^21 also ends with 03 and if N^1 ends with 13, then N^21 also ends with 13).
Hence 20032003  can be written as (200320)100 x 20033.
(….03)(….027)
=>ends with …..081
Hence the tens digit is 8.

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