What is the remainder when 10 to the 99 th power is divided by 9
look for a pattern ...
10^0 ÷ 9 leaves a remainder of 1
10^1 ÷ 9 leaves a remainder of 1
10^2 ÷ 9 leaves a remainder of 1
10^3 ÷ 9 leaves a remainder of 1
....
10^99 ÷ 9 leaves a remainder of 1
Let n be the exponent.
Formula- 10^n/9=1
Pattern can be n+1
To find the remainder when 10^99 is divided by 9, we can first observe a pattern in the powers of 10 modulo 9.
If we list the powers of 10 modulo 9, we can see that:
10^1 ≡ 1 (mod 9)
10^2 ≡ 1 (mod 9)
10^3 ≡ 1 (mod 9)
...
10^99 ≡ 1 (mod 9)
By examining this pattern, we can conclude that any power of 10 is congruent to 1 modulo 9.
Therefore, when 10^99 is divided by 9, the remainder is 1.