base 10 check?

Question

The question asked to covert a number given in base ten to a number in a base 8: The example below used the number 250, can anyone check for errors of any kind?

250 base 10 to 250 base 8

8 250
8 31r2
8 3r 7

Therefore: 7 2 base 8

Answer 1

250 < 8^3 = 512, so 250 has at most 3 digits in base 8:

250 = a*8^2 + b*8^1 + c*8^0 = 64a + 8b + c.

250/8^2 = 250/64 = 3, remainder 58
58/8^1 = 58/8 = 7, remainder 2
2/8^0 = 2/1 = 2, remainder 0

Therefore 250 = 3*8^2 + 7*8^1 + 2*8^0 = 372 base 8.

Answer 2

The place values for base 8 are 1 (8^0), 8 (8^1), 64 (8^2), etc.

The most 64s that fit into 250 is 3 (192)

Subtract this from 250 and get 58. The most 8s that fit into 58 is 7 (56). Subtract this from 58 and get 2.

So 250 (10) = 372 (8)

Answer 3

answer is incorrect.
why didn't you do the last step?
divide that last three by 8 to get 0 r3
when you get that zero, that is the flag to stop

thus the answer is 372 base 8

although James' answer above is correct, he chose the more tedious method. i showed you where you made your mistake, so i hope true learning occurred. i know you'd give me more points, but yahoo limits it to 10.

to help you better understand your method, consider
372 base 8 and what happens when you divide it by 8
you get 37.2 (same principle as 586 base 10 divided by 10 gives 58.6)
that .2 represents 2/8 or a remainder of 2
by continually dividing by the base you shift the least significant digit out as the remainder

372
37 r2
3 r7
0 r3

now that we have 0 we stop (i.e. when the quotient is zero, not the remainder), otherwise we will keep getting
0 r0, which is mathematically correct because all those higher positions in the number are zero.
0372
00372
000372
are all the same number, but in our conversion algorithm we don't have to keep dividing 0 by 8 to figure out that the next "leading zero" is in fact zero