fractional number in a certain mode: what is (1/2)^1000 in mode 9?

[ketanco]

what is (1/2)^1000 in mode 9?

I tried dividing 2 by 9, then 4 by 9, then 8 by 9 etc.... and get the remainders in each one....
(although these are decimals but i assume it is ok?) and after 2^-7 it repeats, so it means every 6 exponent is one group, so i divided 1000 by 6 and it gives remainder of 4, and then read what 2^-4 was, which was 7 but the answer says it should be 4... what am i missing?

 

[Dr.Peterson]

what is (1/2)^1000 in mode 9?

I tried dividing 2 by 9, then 4 by 9, then 8 by 9 etc.... and get the remainders in each one....
(although these are decimals but i assume it is ok?) and after 2^-7 it repeats, so it means every 6 exponent is one group, so i divided 1000 by 6 and it gives remainder of 4, and then read what 2^-4 was, which was 7 but the answer says it should be 4... what am i missing?

Do you mean "modulo 9" (mod 9)?

If so, then you should be learning modular arithmetic, and should know that only integers can be used. In fact, we don't normally mention division at all in this context, though division can be done sometimes.

What is the context of your question? What have you learned about the subject?

 

[ketanco]

Do you mean "modulo 9" (mod 9)?

If so, then you should be learning modular arithmetic, and should know that only integers can be used. In fact, we don't normally mention division at all in this context, though division can be done sometimes.

What is the context of your question? What have you learned about the subject?

modular artihmetic yes

i know what it means. (what i know about it? hmmmm...... example : 3 = 3 in mode 6 but it is 1 in mode 2.... convincing? )

i only can not determine how we treat decimals in modular artihmetic. this is a legitimate exam question