This would be 7 times 64 (8^2) + 7 times 8 + 7 = 511.
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503 base 10 = 767 base 8 503 base 8 = 323 base 10
777 divided by 8 is 97.13 or 97 with remainder 1
97.125
In base eight, the counting numbers are represented as follows: 1, 2, 3, 4, 5, 6, 7, 10, 11, 12. The numbers 1-7 are the same as in base ten, but the number 8 is represented as 10 in base eight, and the pattern continues from there. This is because in base eight, each place value represents a power of 8 instead of 10 as in base ten.
Well, darling, to convert 19 in base 10 to base 8, you divide 19 by 8 to get 2 with a remainder of 3. Then you take that remainder and slap it in front of the 2 to get 23 in base 8. Voila! Math made fabulous.